Question 1 : A light string of 70 cm has its two ends tied at the same level 50 cm apart. A force of 100 N is applied at a distance of<br/> 30 cm from <em>P</em>. The tension in part <em>PR</em> is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c098f1a5a149feab9976"/>
Question 2 : The block A in Figure weighs 100 N. The coefficient of static friction between the block and the table is 0.25. The weight of the block B is maximum for the system to be in equilibrium. The value of T<sub>1</sub> is<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75f13b491ec9580069869c' height='116' width='161' >
Question 3 :
In a rocket of mass {tex} 1000 \mathrm { kg } {/tex} fuel is consumed at a rate of {tex} 40 \mathrm { kg } / \mathrm { s } {/tex}. The velocity of the gases ejected from the rocket is {tex} 5 \times 10 ^ { 4 } \mathrm { m } / \mathrm { s } {/tex}. The thrust on the rocket is
Question 4 :
A lift accelerated downward with acceleration {tex} ^ { \prime } a' {/tex}. {tex} A {/tex} man in the lift throws a ball upward with acceleration {tex} a _ { 0 } \left( a _ { 0 } < a \right) . {/tex} Then acceleration of ball observed by observer, which is on earth, is
Question 5 : A man of mass m = 60 kg is standing on weighing machine fixed on a triangular wedge of angle θ = 60<sup>0</sup> with horizontal as shown in the figure. The wedge is moving up with an upward acceleration a = 2 m/s<sup>2</sup>. The weight registered by machine is<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ecdb4389b1556ddf05c9' height='87' width='153' >
Question 6 :
On the horizontal surface of a truck {tex} ( \mu = 0.6 ) , {/tex} a block of mass {tex} 1 \mathrm { kg } {/tex} is placed. If the truck is accelerating at the rate of {tex} 5 \mathrm { m } / \mathrm { sec } ^ { 2 } {/tex} then frictional force on the block will be
Question 7 :
A bomb of mass 12 kg is dropped by a fighter plane moving horizontally with a speed of 100 ms<sup>–1</sup> from a height of 1 km from the ground. The bomb exploded after 10s into two pieces of masses in the ratio 1 : 5. If the small part started moving horizontally with a speed of 600 ms<sup>–1</sup> the speed of bigger part will be (g = 10 ms<sup>–2</sup>)
Question 8 :
A lift is moving down with acceleration {tex} a {/tex} . A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively
Question 9 : Block A of mass 35 kg is resting on a frictionless floor. Another block B of mass 7 kg is resting on it as shown in figure. The coefficient of friction between the blocks is 0.5 while kinetic friction is 0.4. If a force of 100 N is applied to block B, the acceleration of the block A will be : (g = 10 m s<sup>-2</sup>) <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ed9a4389b1556ddf0672' height='99' width='115' >
Question 10 : Two masses m and M are lying on a surface moving with acceleration a. Only the given supporting and moving surface has coefficient of friction as μ. The frictional forces for μ> a/g and μ < a/g are <br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ec424389b1556ddf053b' height='139' width='197' >
Question 11 : A light rope passes over a pulley. One section of the rope is held by a child and the other section by a man, then <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ec62b5f89758f2d4f477' height='105' width='49' >
Question 12 : In the given arrangement pulleys and string are massless and frictionless and all surfaces are smooth. Find the magnitude of acceleration of wedge of mass <em>M</em>. <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c10bf1a5a149feab99c3"/>
Question 13 :
A cricket ball of mass {tex} 250 \mathrm { g } {/tex} collides with a bat with velocity {tex} 10 \mathrm { m } / \mathrm { s } {/tex} and returns with the same velocity within {tex}0.01{/tex} second. The force acted on bat is
Question 14 : A weight W is lifted by applying a force F as shown in Fig. Find F in terms of W. Assume constant velocity. <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ec194389b1556ddf0515' height='168' width='256' >
Question 15 :
A rocket has a mass of 100 kg. 90% of this is fuel. It ejects fuel vapours at the rate of 1 kg/sec with a velocity of 500 m/sec relative to the rocket. It is supposed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is
Question 16 :
The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius {tex} R {/tex} and coefficient of staic fricular {tex} \mu , {/tex} is
Question 17 :
An elevator weighing {tex} 6000 \mathrm { kg } {/tex} is pulled upward by a cable with an acceleration of {tex} 5 \mathrm { ms } ^ { - 2 } {/tex}. Taking {tex} g {/tex} to be {tex} 10 \mathrm { ms } ^ { - 2 } {/tex}, then the tension in the cable is
Question 18 :
A body of {tex} 5 \mathrm { kg } {/tex} weight kept on a rough inclined plane of angle {tex} 30 ^ { \circ } {/tex} starts sliding with a constant velocity. Then the coefficient of friction is (assume {tex} \left. g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 19 :
If rope of lift breaks suddenly, the tension exerted by the surface of<br>lift {tex} ( a = \text { acceleration of lift } ) {/tex}<br>
Question 20 :
A cylinder of {tex} 10 \mathrm { kg } {/tex} is sliding in a plane with an initial velocity of {tex} 10 \mathrm { m } / \mathrm { s } {/tex}. If the coefficient of friction between the surface and cylinder is {tex}0.5{/tex} then before stopping, it will
Question 21 : A block <em>Q</em> of mass <em>M</em> is placed on a horizontal frictionless surface <em>AB</em> and a body <em>P</em> of mass <em>m</em> is released on its frictionless slope. As <em>P</em> slides by a length <em>L</em> on this slope of inclination θ, the block <em>Q</em> would slide by a distance<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c1efbfef6349df00fe19"/>
Question 22 :
A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25 then the maximum fraction of length of chain that can overhang on edge of table is
Question 23 : Two carts of masses {tex} 200 \mathrm { kg } {/tex} and {tex} 300 \mathrm { kg } {/tex} on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails are same. If the {tex} 200 \mathrm { kg } {/tex} cart travels a distance of {tex} 36 \mathrm { m } {/tex} and stops, then the distance travelled by the cart weighing {tex} 300 \mathrm { kg } {/tex} is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dbd57a2ec8cf4127b93079c"><br>
Question 25 :
A brick of mass {tex} 2 \mathrm { kg } {/tex} begins to slide down on a plane inclined at an angle of {tex} 45 ^ { \circ } {/tex} with the horizontal. The force of friction will be
Question 26 :
A light spring balance hangs from the hook of the other light spring balance and a block of mass $M$ kg hangs from the former one. Then the true statement about scale reading is
Question 27 :
A batsman hit back a ball straight in the direction of the bowler without changing its initial speed of $12{ ms }^{ -1 }$. If the mass of the ball is $0.15 kg$, the impulse imparted to the ball is
Question 28 :
You apply a 75-N force to pull a child's wagon across the floor at a constant speed of 0.5 m/s. If you increase your pull to 90 N ,the wagon will
Question 29 :
A car of mass 1000 kg rounds a curve of radius 250 m at 90 km/hr. Cpmpute its,
Question 30 :
A car has to move on a level turn of radius $45m$. If the coefficient of static friction between the tyre and the road is $\mu_s = 2.0$, find the maximum speed the car can take without skidding.
Question 31 :
A $7 kg$ object is accelerating to the right at $2 km/s$.what is the rightward net force acting on it?
Question 32 : The system shown in the figure is in equilibrium. Masses m<sub>1</sub> and m<sub>2</sub> are 2 kg and 8kg respectively. Spring constants k<sub>1</sub> and k<sub>2</sub> are 50 N/m and 70 N/m respectively. If the compression in second spring is 0.5 m. What is the compression in first spring ? (Both springs have the same natural length) -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ee2cb5f89758f2d4f60e' height='179' width='107' >
Question 33 :
A man weighing $80\ kg$ is standing at the centre of a flat boat and he is $20\ m$ from the shore. He walks $8\ m$ on the boat towards the shore and then halts. The boat weight $200\ kg$. How far is he from the shore at the end of this time?
Question 35 :
A block of weight $100$ $N$ is lying on a rough horizontal surface. If coefficient of friction $\cfrac{1}{\sqrt{3}}$. The least possible force that can move the block is
Question 36 :
When an axle rotates in a sleeve, the friction involved in the process is
Question 37 :
A block of mass {tex} 10 \mathrm { kg } {/tex} is placed on a rough horizontal surface having coefficient of friction {tex} \mu = 0.5 . {/tex} If a<br>horizontal force of {tex} 100 N {/tex} is acting on it, then acceleration<br>of the block will be
Question 38 :
If the normal force is doubled, the co-efficient of friction is?
Question 39 :
A ball of mass <em>m</em> falls vertically from a height <em>h</em> and collides with a block of equal mass moving horizontally with velocity <em>v</em> on a smooth surface. The co-efficient of kinetic friction between the block and ball is 0.2 and co-efficient of restitution is 0.5. The difference in velocity of block before and after collision, is
Question 41 :
Assertion: In order to reduce sliding friction, lubricants are used.
Reason: Lubrication changes the conditions of rubbing, replacing the sliding friction by rolling friction, there by reducing the force of friction.
Question 42 :
Value of $\theta$ is increased gradually from $\theta$ = 0. At $\theta = tan^{-1} (\frac{1}{2})$ both the blocks just start slipping. Than value of $\mu_2$ is : (g = 10 m/$s^2$):
Question 43 :
With what minimum acceleration can a fireman slide down a rope whose breaking strength is two third of his weight ?
Question 45 :
A block of mass $2 kg$ is placed on the floor. The coefficient of static friction is $0.4$. Force of $2.8N$ is applied on the block. The force of friction between the block and the floor is (Taken $g = 10m/s^2$)<br/>
Question 46 :
A ware house worker exerts a constant horizontal force of magnitude $85\ N$ on a $40kg$ box that is initally at rest on the floor of the ware house. After moving a distance of $2m$ the speed of the box is $1 \ ms^{-1}$. The coefficent of friction between the box and the ware house floor is $(g=10ms^{-2})$
Question 48 :
A body slipping on a tough horizontal plane moves With a deceleration of 4.0 m/${ s }^{ 2 }$ . What is the coefficient of kinetic friction between the block and the plane ?
Question 49 :
A block of $1\ kg$ is stopped against a wall by applying a force $F$ perpendicular to the wall. If $\mu=0.2$ then minimum value of $F$ will be :
Question 50 :
To avoid slipping while walking on ice, one should take smaller steps because:<br>
Question 51 :
The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough $A$ body starting from the rest at top come back to rest at the bottom, then the coefficient of friction for the lower half is given by _______.
Question 52 :
A particle attached to a string is rotating with a constant angular velocity and its momentum is $L$. If the string is halved and angular velocity is kept constant, the angular momentum will be
Question 53 :
The limiting value of static friction between two contact surfaces is :
Question 54 :
A stick of {tex} 1 \ m {/tex} is moving with velocity of {tex} 2.7 \times 10 ^ { 8 } \mathrm { ms } ^ { -1 } . {/tex} What is the apparent length of the stick {tex} \left( c = 3 \times 10 ^ { 8 } \mathrm { ms } ^ { - 1 } \right) {/tex}
Question 55 :
A block of mass 2 kg rests on a rough inclned plane making am angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plans is 0.7. The frictional force on the block is $(g = 9.8 m/s^2)$ :
Question 56 :
A body of mass $3\ kg$ is moving along a straight line with a velocity of $24\ {ms}^{-1}$. When it is at appoint $'P'$ a force of $9\ N$ acts on the body in a direction opposite to its motion. The time after which it will be at $'P'$ again is:
Question 57 :
The mass of a lift is 500 kg. When it ascends with an acceleration of {tex} 2 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex}, the tension in the cable will be {tex} \left[ \mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right] {/tex}
Question 58 : Two trolleys 1 and 2 are moving with acceleration a<sub>1</sub> and a<sub>2</sub> respectively in the same direction. A block of mass 'm' on trolleys 1 is in equilibrium from the frame of observer stationary w.r.t. trolleys 2. The magnitude of friction on block due to trolley is -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ed85491ec95800698533' height='66' width='206' >
Question 59 :
A body of mass 40 gram is moving with a constant velocity of 20 $ms^{-}$ $^{1}$ on a horizontal frictionless table. The force acting on the body in horizontal direction is:
Question 60 :
A body is rolling on the ground with a velocity of $1\ m/s$. After travelling a distance of $5\ m$, the body stops. The coefficient of friction is:
Question 61 :
While using travelling microscope in an experiment one find that one main scale division length is 1 mm and 10 VSD = 9 MSD. When this microscope is focused over a glass slab which is placed over a spot. Then which of the reading is correctly written in terms of significant figure
Question 62 :
The distance of a galaxy from the earth is of the order of 10<sup>25 </sup>m. The time taken by light to reach the earth from the galaxy is
Question 63 :
Wavelength of ray of light is {tex} 0.00006 \mathrm { m } {/tex}. It is equal to
Question 64 :
According to Newton, the viscous force acting between liquid layers of area {tex} \mathrm { A } {/tex} and velocity gradient {tex} \Delta v / \Delta z {/tex} is given by {tex} F = - \eta A \frac { \Delta v } { \Delta z } {/tex} where {tex} \eta {/tex} is constant called coefficient of viscosity. The dimension of {tex} \eta {/tex} are
Question 68 :
If θ<sub>1</sub> = (10 ± 0.1)<sup>0</sup>C and θ<sub>2</sub> = (20 ± 0.4)<sup> 0</sup>C, then θ<sub>2</sub> - θ<sub>1</sub> = .....
Question 70 :
A wire is of mass (0.3 ± .003) gm. The radius is (0.5 ± 0.005) cm and length is (6 ± .06) cm. The maximum percentage error in density is -
Question 71 :
In acertain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and unit of length is 10 m. In this system, one unit of power will correspond to
Question 72 :
Given that force (F) is given F = Pt<sup>-1</sup> + Qt. Here t is time. The unit of P is same as that of -
Question 73 :
Which of the following is not the name of a physical quantity
Question 74 :
The resistance {tex} R = \frac { V } { i } {/tex} where {tex} V = 100 \pm 5 {/tex} volts and {tex} i = 10 \pm 0.2 {/tex} amperes. What is the total error in {tex} R {/tex}
Question 78 :
A current of 2.34 ampere flows in a resistance of 11.111111 Ω. The potential difference across the given resistance with due regard for significant figures is -
Question 81 :
{tex}\mathbf {Assertion}{/tex} : Light year and year, both measure time .<br>{tex}\mathbf {Reason}{/tex} : Because light year is the time that light takes to reach the earth from the sun.
Question 82 :
The dimensional formula for impulse is same as the dimensional formula for
Question 84 :
The correct value of {tex} 0 ^ { \circ } \mathrm { C } {/tex} on the Kelvin scale is
Question 87 :
The acceleration of a particle as seen from two frames {tex} S _ { 1 } {/tex} and {tex} S _ { 2 } {/tex} has equal magnitude {tex} 5 \mathrm { ms } ^ { - 2 } . {/tex}
Question 88 :
The current voltage relation of diode is given by {tex}I =(e1000 V/T- l) mA{/tex}, where the applied voltage {tex} V{/tex} is in volts and the temperature {tex}T{/tex} is in degree Kelvin. If a student makes an error measuring {tex} ± 0.01 V{/tex} while measuring the current of {tex} 5 mA{/tex} at {tex}300 K,{/tex} what will be the error in the value of current in {tex}mA?{/tex}
Question 90 :
A man starts from {tex} O {/tex} moves 500{tex} \mathrm { m } {/tex} turns by {tex} 60 ^ { \circ } {/tex} and moves 500{tex} \mathrm { m } {/tex} again turns by {tex} 60 ^ { \circ } {/tex} and moves 500{tex} \mathrm { m } {/tex} and so on. Find the displacement after (i){tex} 5{tex} \mathrm { th } {/tex} turn, (ii) {tex}3{tex} \mathrm { rd } {/tex} turn
Question 91 :
The dimension of quantity {tex} ( L / R C V ) {/tex} is
Question 92 :
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3{tex} \% {/tex} each, then error in the value of resistance of the wire is
Question 93 :
The speed of light {tex} ( c ) , {/tex} gravitational constant {tex} ( G ) {/tex} and Planck's constant {tex} ( h ) {/tex} are taken as the fundamental units in a system. The dimension of time in this new system should be
Question 94 :
Two capacitors {tex} C _ { 1 } = 5.2 \mu F{/tex} and {tex} 0.1 \mu F{/tex} and {tex} C _ { 2 } = 12.2 \mu F {/tex} are joined (i) In series (ii) In parallel. Find the net capacitance in these two cases.
Question 95 :
The velocity of surface waves depends upon surface tension, coefficient of viscosity and density. The relation is
Question 96 :
If the constant of gravitation {tex} ( G ) , {/tex} Planck's constant {tex} ( h ) {/tex} and the velocity of light {tex} ( c ) {/tex} be chosen as fundamental units. The dimension of the radius of gyration is
Question 97 :
Two resistances of 400 {tex}\Omega{/tex} and 800 {tex}\Omega{/tex} connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance 10,000 {tex}\Omega{/tex} is used to measure the potential difference across 400 {tex}\Omega{/tex}. The error in the measurement of potential difference in volts approximately is
Question 98 :
Which of the following units denotes the dimensions {tex} \left[ M L ^ { 2 } / Q ^ { 2 } \right] , {/tex} where {tex} Q {/tex} denotes the electric charge?
Question 100 :
If velocity {tex} v {/tex}, acceleration {tex} A {/tex} and force {tex} F {/tex} are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of {tex} v , A {/tex} and {tex} F {/tex} would be
Question 101 :
A dust particle oscillates in air with a time period which depends on atmospheric pressure P, density of air d and energy of the particle E, then time period is proportional to
Question 102 :
The least count of a stop watch is 1/5 second. The time of 20 oscillations of a pendulum is measured to be 25 seconds. The minimum percentage error in the measurement of time will be
Question 103 :
If a copper wire is stretched to make its radius decrease by 0.1{tex} \% {/tex}, then the percentage increase in resistance is approximately
Question 104 :
Which of the following quantities has the SI unit kg m<sup>2</sup> s<sup>-3 </sup>A<sup>-2</sup>?
Question 105 : In Fig. shown find the velocity of block {tex} m {/tex} if both the rope ends are pulled with {tex} a {/tex} velocity {tex} v {/tex} .<br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e8ac286131a2b237d875c76' class="uploaded-image" />
Question 106 :
The value of {tex} n {/tex} so that vectors {tex} 2 \hat { i } + 3 \hat { j } - 2 \hat { k } , 5 \hat { i } + n \hat { j } + \hat { k } {/tex} and {tex} - \hat { i } + 2 \hat { j } + 3 \hat { k } {/tex} may be coplanar, will be
Question 107 :
Two forces {tex} \vec { F } _ { 1 } = 500 \mathrm { N } {/tex} due east and {tex} \vec { F } _ { 2 } = 250 \mathrm { N } {/tex} due north have their common initial point. {tex} \vec { F } _ { 2 } - \vec { F } _ { 1 } {/tex} is
Question 108 :
The projection of a vector {tex} \vec { r } = 3 \hat { i } + \hat { j } + 2 \hat { k } {/tex} on the {tex} x - y {/tex} plane has magnitude
Question 109 :
If velocity, force and time are taken to be fundamental quantities find dimensions formula for (a) mass
Question 112 :
{tex}Assertion:{/tex} Specific gravity of a fluid is a dimensionless quantity
<br>{tex}Reason: {/tex} It is the ratio of density of fluid to density of water.
Question 113 :
Calculate the area of the triangle determined by the two vectors {tex} \vec { A } = 3 \hat { i } + 4 \hat { j } {/tex} and {tex} \vec { B } = - 3 \hat { i } + 7 \hat { j } {/tex}
Question 114 : What is the final reading of callipers as shown -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c65b4389b1556ddef620' height='97' width='176' >
Question 116 :
Given {tex} \vec { A } = 2 \hat { i } + p \hat { j } + q \hat { k } {/tex} and {tex} \vec { B } = 5 \hat { i } + 7 \hat { j } + 3 \hat { k } . {/tex} If {tex} \vec { A } \| \vec { B } , {/tex} then the values of {tex} p {/tex} and {tex} q {/tex} are, respectively,
Question 117 :
A sample of gas is at 0°C. To what temperature it must be raised in order to double the r.m.s. speed of the molecule-
Question 118 :
Which of the following physical quantities has same unit in all the three system of units?
Question 119 : Match the Column I with Column II <table><tr><th>Column I Physical quantity</th> <th>Column II Name of unit</th> </tr><tr><td>(A) Conductance</td> <td>(p) Gray</td> </tr> <tr><td>(B) Magnetic induction </td> <td>(q) Lumen</td> </tr> <tr><td>(C) Absorbed dose</td> <td>(r) Tesla</td> </tr> <tr><td>(D) Luminous flux</td> <td>(s) Siemens</td></tr></table>
Question 120 :
The dimensions of h/e (h = Planck's constant and e = electronic charge) are same as that of :
Question 121 :
Pitch of a screw gauge is 0.5 mm and its least count is 0.01 mm. Calculate no. of divisions on its head scale.
Question 122 :
Dimensions of one or more pairs are same. Identify the pairs-
Question 123 :
A screw gauge with a pitch of {tex} 0.5mm{/tex} and a circular scale with 50 divisions is made to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is {tex} 0.5mm {/tex} and the 25th division coincides with the main scale line.
Question 124 : The velocity of a particle is given by v = a + <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c571b5f89758f2d4e454' height='37' width='15' > + ct<sup>2</sup><br>The unit of b will be
Question 126 :
An unknown liquid at a high temperature is safely mixed with normal water until an equilibrium temperature is reached. Some heat is gained by the cold water. Identify by which of the following law this can be explained ?
Question 128 :
The first law of thermodynamics is derived from which of the following law ? <br/>
Question 131 :
State whether given statement is True or False<br/>Heat brings about a change in the state of matter.
Question 135 :
In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases 20 J of heat and 8 J of work is done on the gas if the initial internal energy of the gas was 30 J. The final internal energy wilI be:
Question 136 :
Which physical quantity determines the direction of flow of heat energy?<br/>
Question 137 :
In a certain process $500\ cal$ of heat is given to a system and the system does $100\ J$ of work. The increase in internal energy of the system is
Question 140 :
A gas obeying the equation of state $PV = RT$ undergoes a hypothetical reversible process described by the equation, $PV^{5/3}exp \left (-\dfrac {PV}{E_{0}}\right ) = C_{1}$ where $C_{1}$ and $E_{0}$ are dimensioned constants. Then, for this process, the thermal compressibility at high temperature.
Question 141 :
Which of the following is a restatement of first law of thermodynamics:
Question 142 :
One mole of ${O}_{2}$ gas having a volume equal to 22.4 liters at $0^oC$ and 1 atmospheric pressure is compressed isothermally so that its volume reduces to 11.2 liters. The work done in this process is then<br>
Question 144 :
Identify which of the following statement does NOT apply to the First Law of Thermodynamics?<br/>
Question 145 :
State whether true or false :<br>During the change of state, the temperature does not change.
Question 146 :
When heat is added to a system, which of the following is not possible? <br/>
Question 147 :
A gas expands 0.25 $\mathrm { m } ^ { 3 }$ at constant pressure 10$ ^ { 3 } \mathrm { N } / \mathrm { m } ^ { 2 } ,$ the work done is
Question 148 :
Heating of a wheel on applying brakes is due to the relation
Question 150 :
If $1 cal = 4.2 J$, then $0.2 cal g^{-1} {\;}^oC^{-1}=......... J kg^{-1} K^{-1}$
Question 151 :
At equilibrium temperature, the rate of flow of heat energy from one body to the other and back is the same. Is the statement True or False
Question 152 :
When heat energy is given out by a hot substance then the kinetic energy of its molecules _________. Fill in the blank. <br/>
Question 154 :
When water is heated from 0 $^{\circ} C$ to 4$ ^{\circ} C$, it :
Question 156 :
According to law of conservation of energy, heat energy is transformed into which two types of energy?<br>
Question 157 :
A cylinder with fixed capacity of $67.2$ lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by $20^0C$ is :
Question 158 :
Consider the following two statements and choose the correct answer :<br>A) If heat is added to a system its temperature must always increase<br>B) If positive work is done by a system in thermodynamic process its volume must increase.<br>
Question 159 :
1 mole of an ideal gas STP is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy $(\gamma = 1.4)$
Question 160 :
Work done in converting 1 g of ice at $- 10^o$C into steam at $100^o$C is
Question 161 :
A solid cube and a solid sphere of identical material and equal masses are heated to the same temperature and left to cool in the same surroundings. Then
Question 162 :
The work done in which of the following process is zero
Question 163 :
A gas expands under constant pressure P from volume $V_{2}to V_{1}$. The work done by the gas is
Question 164 :
A sample of $0.1\ g$ of water at $100^{o}\ C$ and normal pressure $(1.013\times 10^{5}\ Nm^{-2})$ requires $54$ cal of heat energy of convert to steam at $100^{o}\ C$. If the volume of the steam produced is $167.1\ cc$, the change in internal energy of the sample, is?
Question 165 :
Heat of $20\ Kcal$ is supplied to the system and $8400\ J$ of external work is done on the system so that its volume decreases at constant pressure. The change in internal energy is ($J=4200\ J/kcal$)
Question 166 :
In a thermodynamic process two moles of a monatomic ideal gas obeys P $\propto V^{-2}$. If temperature of the gas increases from 300 K to 400 K, then find work done by the gas (where $R=$universal gas constant)
Question 167 : <div>Gas in a container absorbs 300 J of heat. After this, 100 J of work is done on it which is followed by 50 J of work done by the gas. The increase in the internal energy of the gas is:</div>
Question 168 : A cylinder of mass $1$kg is given heat of $20000$J at atmospheric pressure. If initially, temperature of a cylinder is $20^o$C, find work done by the cylinder.<div> (Given that Specific heat capacity of cylinder $=400$J $kg^{-1}$ $^0C^{-1}$, Coefficient of volume expansion $=9\times 10^{-5}$ $^0C^{-1}$, Atmospheric pressure $=10^5$ $N/m^2$ and Density of cylinder $=9000$ $kg/m^3$).<br/></div>
Question 169 :
Internal energy of $ n_{1} $ mol of hydrogen of temperature $ T $ is equal to the internal energy of $ n_{2} $ mol of helium at temperature $ 2 T . $ The ratio $\dfrac{ n_{1} }{ n_{2}} $ is
Question 171 : $1\ litre$ of an ideal gas $(\gamma = 1.5)$ at $300\ K$ is suddenly compressed to half its original volume.<br/>If the original pressure is $100\ kPa$, find the work done by the gas in the process .<div>Take: $\sqrt 2=1.41$</div>
Question 172 :
An ideal diatomic gas is expanded so that the amount of heat transferred to the gas is equal to the decrease in its internal energy.<br>If in the above process, the initial temperature of the gas to be $T_0$ and the final volume be 32 times the initial volume, the work done by the gas during the process will be in joules:
Question 173 :
During an isothermal expansion, a confined ideal gas does 150 J of work against its surroundings. This implies that:
Question 174 :
The internal energy of a solid also increases when the heat is transferred to its surroundings. A 5 kg solid bar is heated at atmospheric pressure. Its temperature increases from $20^{0}C$ to $70^{0}C$. The linear expansion coefficient of solid bar is $ 1 \times 10^{-3}/C^{0}$. The density of a solid bar is 50 kg/$m^{3}$. The specific heat capacity of a solid bar is 200 J/kg C$^{0}$. The atmospheric pressure is $ 1 \times 10^{5} N/m^{2}$.<br/> The work done by the solid bar due to thermal expansion, under atmospheric pressure, is
Question 175 :
Find the change in internal energy in joule when 10$\mathrm { g }$ of air is heated from $30 ^ { \circ } \mathrm { C }$ to $40 ^ { \circ } \mathrm { C }$
Question 176 :
Consider a rectangular block of wood moving with a velocity $v_0$ in a gas at temperature T and mass density $\rho$. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to $v_0$ is A. The drag force on the block is (where m is the mass of the gas molecule).
Question 177 :
An insulated container containing monoatomic gas of molar mass m is moving with a velocity $v_0$. If the container is suddenly stopped. The change in temperature is?
Question 178 :
A thermally insulated rigid container contains an ideal gas. It is heated through a resistance coil of 100$\Omega $ by passing a current of 1 A for five minutes, then change in internal energy of the gas is<br/>
Question 180 :
An iron block of mass $2\;kg$, falls from a height of $10m$. After colliding with the ground it loses $25\%$ energy to surroundings and rest is gained as heat. Then find the temperature rise of the block. (Take sp. heat of iron $470\;J/kg^{\circ}C$)<br/>
Question 181 :
Two identical containers $ A $ and $ B $ have frictionless pistons. They contain the same volume of an ideal gas at the same temperature. The mass of the gas in $ A $ is $ m_{A} $ and that in $ B $ is $ m_{B} $. The gas in each cylinder is now allowed to expand isothermally to double the initial volume. The change in the pressure in $ A $ and $ B $, respectively, is $ \Delta p $ and $ 1.5 \Delta p $ Then
Question 182 :
An ideal gas is subjected to cyclic process involving four thermodynamic states, the amounts of heat (Q) and work (W) involved in each of these states are<br>$Q_1\,=\,6000\,J,$<br>$Q_2\,=\,-\,5500\,J;$<br>$Q_3\,=\,-\,3000\,J;$<br>$Q_4\,=\,3500\,J$<br>$W_1\,=\,2500\,J;$<br>$W_2\,=\,-\,1000\,J;$<br>$W_3\,=\,-\,1200\,J;$<br> $W_4\,=\,x\,J.$<br>The ratio of the net work done by the gas to the total heat absorbed by the gas is . The values of $\times$ and $\eta$ respectively are<br>
Question 183 :
In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20J$ of heat and $8J$ of work is done on the gas. If initial internal energy of the gas was $30J$, what will be the fixed internal energy?
Question 184 :
Two cylinders A and B fitted with pistons contain an equal number of moles of an ideal monoatomic gas at $400 K$. The piston of A is free to move while that of B is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is $42 K$, the rise in temperature of the gas in B is
Question 185 :
Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\ K$. The piston of $A$ is free to move, while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30\ K$, then the rise in temperature of the gas in $B$ is<br>
Question 186 :
Find the external work done by the system inkcal, when 20 keal of heat is supplied to thesystem and the increase in the internal energy is 8400$\mathrm { J } ( \mathrm { J } = 4200 \mathrm { J } / \mathrm { kcal } ) ?$
Question 187 :
STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work.<br/><br/>STATEMENT-2: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.
Question 189 :
The mass of the earth is 81 times that of the moon and the radius of the earth is 3.5 times that of the moon. The ratio of the acceleration due to gravity at the surface of the moon to that at the surface of the earth is
Question 190 :
Two planets at mean distance {tex} d _ { 1 } {/tex} and {tex} d _ { 2 } {/tex} from the sun and their frequencies are {tex} n {/tex} and {tex} n {/tex} respectively then
Question 191 :
The depth at which the effective value of acceleration due to gravity is {tex} \frac { g } { 4 } {/tex} is<br>
Question 192 :
The acceleration due to gravity at pole and equator can be related as
Question 193 :
An artificial satellite moving in a circular orbit around the earth has a total energy <em>E</em><sub>0</sub> (KE+PE). Its PE is
Question 194 :
A person sitting in a chair in a satellite feels weightless because
Question 195 :
At the surface of a certain planet, acceleration due to gravity is one- quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct
Question 196 :
Orbital velocity of earth's satellite near the surface is {tex} 7 \mathrm { km } / \mathrm { s } {/tex}. When the radius of the orbit is {tex} {4} {/tex} times than that of earth's radius, then orbital velocity in that orbit is
Question 198 :
If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is
Question 199 :
A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of earth
Question 200 :
Out of the following, the only incorrect statement about satellites is
Question 201 :
The acceleration of a body due to the attraction of the earth (radius {tex} R {/tex} ) at a distance {tex} 2 R {/tex} from the surface of the earth is {tex} ( g = {/tex} acceleration due to gravity at the surface of the earth)
Question 202 :
Escape velocity on earth is {tex} 11.2 \mathrm { km } / \mathrm { s } {/tex}. What would be the escape velocity on a planet whose mass is {tex} {1000} {/tex} times and radius is {tex} {10} {/tex} times that of earth<br>
Question 203 :
Kepler's second law (law of areas) is nothing but a statement of
Question 204 :
If the height of a satellite from the earth is negligible in comparison<br>to the radius of the earth {tex} R , {/tex} the orbital velocity of the satellite is<br>
Question 205 :
The relay satellite transmits the {tex}\mathrm {T.V.} {/tex} programme continuously from one part of the world to another because its
Question 206 :
Two heavenly bodies {tex} S _ { 1 } {/tex} and {tex} S _ { 2 } , {/tex} not far off from each other are seen to revolve in orbits
Question 207 :
Two spheres of same radius and same material are placed in contact with each other. The gravitational force between them is
Question 209 :
Acceleration due to gravity {tex} \ g {/tex} for a body of mass 'm' on earth's surface is proportional to (Radius of earth-R, mass of earth-M)
Question 210 :
Periodic time of a satellite revolving above Earth's surface at a height equal to {tex} R {/tex}, radius of Earth, is<br>{tex} [ g {/tex} is acceleration due to gravity at Earth's surface]<br>
Question 211 :
Two bodies of masses <em>M</em><sub>1</sub> = <em>m</em> and <em>M</em><sub>2</sub> = 4m are placed at a distance <em>r</em>. The gravitational potential at a point on the line joining them where the gravitational field is zero is
Question 212 :
As we go from the equator to the poles, the value of {tex} g {/tex}
Question 213 :
The eccentricity of earth's orbit is {tex} 0.0167 . {/tex} The ratio of its maximum speed in its orbit to its minimum speed is
Question 214 :
If radius of the earth contracts {tex} 2 \% {/tex} and its mass remains the same, then weight of the body at the earth surface
Question 215 :
A pendulum that beats seconds on the surface of the earth were taken to a depth of $ (1/4) $th the radius of the earth. Its time period of oscillation will be
Question 216 :
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water, the tension in the string is T<sub>0</sub>. Find the difference between tensions when the ship is sailing with a velocity v.
Question 219 :
The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if the entire mass of the shell is
Question 220 :
The ratio of the {tex} K.E. {/tex} required to be given to the satellite to escape earth's gravitational field to the {tex} K.E. {/tex} required to be given so that the satellite moves in a circular orbit just above earth atmosphere is
Question 221 :
{tex}\mathbf {Assertion}{/tex} :The difference in the value of acceleration due to gravity at pole and equator is proportional to square of angular velocity of earth.<br>{tex}\mathbf {Reason}{/tex} : The value of acceleration due to gravity is minimum at the equator and maximum at the pole.
Question 222 :
The masses and radii of the earth and moon are {tex} M _ { 1 } , R _ { 1 } {/tex} and {tex} M _ { 2 } , R _ { 2 } {/tex} respectively. Their centres are distance {tex} d {/tex} apart. The minimum velocity with which a particle of mass {tex} m {/tex} should be projected from a point midway between their centres so that it escapes to infinity is<br>
Question 223 :
Newton's law states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.<br><br>If you throw a ball up in the air, it falls down because of gravitational force of earth. Why doesn't the earth move up if an equal force is exerted on it by the ball ?
Question 224 :
If the radius of earth were shrink by 1%, its mass remaining th same, the acceleration due to gravity on the earth's surface would -
Question 225 :
A mass <em>m</em> is divided into two parts <em>xm</em> and (1 – <em>x</em>)<em>m</em>. For a given separation, the value of <em>x</em> for which the gravitational attraction between the two pieces becomes maximum is
Question 226 :
Four particles each of mass {tex} M , {/tex} are located at the vertices of a square with side {tex} L {/tex}. The gravitational potential due to this at the centre of the square is<br>
Question 227 :
The escape velocity of a body on an imaginary planet which is thrice the radius of the earth and double the mass of the earth is {tex} (v _ { e } {/tex} is the escape velocity of earth)
Question 228 :
A person is standing with his shoes on the ground each shoe having an area of $200$ $cm^2$ in contact with the ground. When he has both feet on the ground he exerts a pressure of $9000$ $Nm^{-2}$. What is the mass of the person?(Take g$=10m/s^2$)
Question 229 :
Assertion: When a soda water bottle falls freely from a height $h$, the gas bubble rises in water from the bottom
Reason: Air is lighter than liquid
Question 230 :
The masses and radii of the earth and moon are <em>M</em><sub>1</sub>, <em>R</em><sub>1</sub> and <em>M</em><sub>2</sub>, <em>R</em><sub>2</sub> respectively. Their centres are at distance <em>d</em> apart. The minimum speed with which a particle of mass <em>m</em> should be projected from a point midway the two centres so as to escape to infinity is
Question 232 : A spherical hole is made in a solid sphere of radius <em>R</em>. The mass of the sphere before hollowing was <em>M</em>. The gravitational field at the centre of the hole due to the remaining mass is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c3acbfef6349df00fef6"/>
Question 233 :
(a) Calculate the speed of the car in km/min during the time
Question 235 : <font>The direction of gravitational intensity at point P of a hemispherical shell of uniform mass density is indicated by the arrow</font></p> <p align="center"> <img style='object-fit:contain' align="bottom" height="65" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0ea384265580f62ccc068" width="125"/> </p>
Question 236 :
<font>Find the work done to take a particle of mass m from surface of the earth to a height equal to 2R.</font></p>
Question 237 :
<font>A coin placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency </font><font face="Symbol, serif"><font></font></font><font>. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time -</font></p>
Question 238 :
<font>A small satellite is revolving near earth's surface. Its orbital velocity will be nearly -</font></p>
Question 239 :
<font>Which of the following Kepler’s laws is also known as harmonic law ?</font></p>
Question 240 :
<font>The tidal wave in the sea are primarily due to gravitational effect of</font></p>
Question 241 :
<font>The escape velocity from the earth is about 11 km/s. The escape velocity from a planet having twice the radius and the same mean density as the earth is -</font></p>
Question 242 :
<font>Which of the following statements is correct regarding the universal gravitational constant G ?</font></p>
Question 243 :
<font>An astronaut experiences weightlessness’ in a space satellite it is because.</font></p>
Question 244 :
<font>Earth is revolving around the sun if the distance of the earth from the sun is reduced to 1/4</font><sup><font>th</font></sup><font> of the present distance then the present length of the day is reduced by</font></p>
Question 245 :
<font>Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because, </font> </p>
Question 246 :
<font>In some region, the gravitational field is zero. The gravitational potential in this region</font></p>
Question 249 :
<font>Both earth and moon are subjected to the gravitational force of the sun. As observed from the sun, the orbit of the moon</font></p>
Question 251 :
<font>The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on -</font></p>
Question 252 :
<font>The escape velocity of a projectile from the earth is approximately -</font></p>
Question 253 :
The length of a second's pendulum at the surface of earth is $1\space m$. The length of second's pendulum at the surface of moon where $g$ is $1/6th$ that at earth's surface is
Question 254 : A particle of mass <em>m</em> is projected with an initial velocity <em>u</em> at angle θ from the ground. What is the work done by gravity during the time it reaches the highest point <em>P</em> is: <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bf5abfef6349df00fcd0"/>
Question 255 :
A point mass moves along a circle of radius R with constant angular acceleration α. How much time is needed after motion begins for the radial acceleration of the point mass to be equal to its tangential acceleration?
Question 256 :
A body of mass accelerates uniformly from rest to velocity <em>V</em><sub>0</sub> in time <em>t</em><sub>0</sub>. What is the instantaneous power delivered to the body when the velocity is {tex}\frac{V_{0}}{2}{/tex}.
Question 257 :
The kinetic energy of particle moving along a circle of radius <em>R</em> depends upon the distance covered S and is given by <em>K</em> = <em>aS</em> where <em>a</em> is a constant. Then the centripetal force acting on the particle is
Question 258 : The relationship between the force <em>F</em> and position <em>x</em> of a body is as shown in figure. The work done in displacing the body from <em>x</em> = 1 m to <em>x</em> = 5 m will be <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bfa1bfef6349df00fd02"/>
Question 259 :
A spring 40 mm long is stretched by the application of a force. If 10 N forces required to stretch the spring through 1mm, then work done in stretching the spring through 40 mm is
Question 260 :
Two identical balls are projected, one vertically up and the other at an angle of 30<font face="Symbol">°</font> with the horizontal, with same initial speed. The potential energy at the highest point is in the ratio
Question 261 :
A heavy uniform chain lies on a horizontal table-top. If the co-efficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang over one edge of the table is
Question 262 : <font>A block of mass m slides along the track with kinetic friction µ. A man pulls the block through a rope which makes an angle </font><font face="Symbol, serif"><font></font></font><font> with the horizontal as shown in the figure. The block moves with constant speed V. Power delivered by the man is </font> </p> <p> <img style='object-fit:contain' align="bottom" height="70" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0ef6ce6377b2e815f4d1e" width="189"/> </p>
Question 263 :
<font>A particle of mass m moving with a velocity v strikes a wall and rebounds back. If the magnitude of the velocity is unchanged, the magnitude of force exerted on the wall by the particle during the time of contact (t) will be - </font> </p>
Question 264 : <font>In the figure shown the potential energy U of a particle is plotted against its position 'x' from origin. Then which of the following statement is correct. A particle at -</font></p> <p> <img style='object-fit:contain' align="bottom" height="116" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0ef90a89a512aab2122f0" width="132"/> </p>
Question 266 :
A particle is hanging from a string of length <em>l</em> = 10 m. It is imparted a velocity of 20 m/s at the bottom. The velocity of the particle at its highest point is
Question 267 :
When a body moves in a circle, the work done by the centripetal force is always
Question 268 :
A block of mass <em>m</em> is moving with a constant acceleration <em>a</em> on a rough plane. If the co-efficient of friction between the block and ground is <font face="Symbol">µ</font>, the power delivered by the external agent after a time <em>t</em> from the beginning is
Question 269 : A block of mass <em>m</em> initially at rest dropped from a height <em>h</em> on to a massless spring of force constant <em>k</em>, the maximum compression in the spring is <em>h</em>/4, then spring constant <em>k</em> is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bfd3f1a5a149feab992b"/>
Question 270 :
A particle of mass <em>m</em> is moving in a circular path of constant radius <em>r</em> such that its centripetal acceleration <em>a<sub>c</sub></em> is varying with time <em>t</em> as <em>a</em><sub><em>c</em></sub> = <em>k</em><sup>2</sup>rt<sup>2</sup>, where <em>k</em> is a constant. The power delivered to the particle by the force acting on it is
Question 271 :
The potential energy of a particle of mass 0.1 kg moving along <em>x</em>-axis is given by <em>U</em> = 5<em>x</em><br/> (<em>x</em> – 4), here <em>U</em> is in Joules and <em>x</em> is in meters. Which of the following is incorrect.
Question 272 :
<font>A block of mass 10 kg is moving in x - direction with a constant speed 10 ms</font><sup><font>-1</font></sup><font>. It is subjected to a retarding force F = -0.1 x J/m during its travel from x = 20 m to x = 30 m. Find the final KE.</font></p>
Question 273 : <font>Two blocks of masses 2 kg and 1 kg respectively are tied to the ends of a string which passes over a light frictionless pulley. The masses are held at rest at the same horizontal level and then released. The distance traversed by centre of mass in 2 s is -(g = 10 m/s</font><sup><font>2</font></sup><font>)</font></p> <p> <img style='object-fit:contain' align="bottom" height="92" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0ef9ba89a512aab21233b" width="93"/> </p>
Question 274 :
<font>The average energy consumed by a human being in a day is:</font></p>
Question 275 :
<font>The work done by a body against friction always results in :</font></p>
Question 276 :
<font>A truck and a car moving with the same kinetic energy are brought to rest by the application of brakes which provide equal retarding forces. Which of them will come to rest in a shorter distance?</font></p>
Question 277 : <font>Consider the following statements A and B. Identify the correct choice in the given answers:</font></p> <p align="justify"> <font>A. In a one dimensional perfectly elastic collision between two moving bodies of equal masses, the bodies merely exchange their velocities after collision</font></p> <p align="justify"> <font>B. If a lighter body at rest suffers perfectly elastic collision with a very heavy body moving with a certain velocity, then after collision both travel with same velocity</font></p>
Question 278 :
<font>When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after collision they will move:</font></p>
Question 279 : In the figure shown, pulley and spring are ideal. If <em>k</em> is spring constant of spring, the potential energy stored in it is (<em>m</em><sub>1</sub> > <em>m</em><sub>2</sub>) <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bfa9f1a5a149feab98fe"/>
Question 280 : A block of mass 3 kg slides down a rough curved path from point <em>A</em> as shown. If it stops at <em>C</em>, the work done by friction is (<em>g</em> = 10 ms<sup>–2</sup>) <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bf71bfef6349df00fce4"/>
Question 281 : A particle initially at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance <em>h</em> below the highest point. Then <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bfd7f1a5a149feab992e"/>
Question 282 : <font>Six identical uniform rods PQ, QR, RS, ST, TU and UP each weighing W are freely joined at their ends to form a hexagon. The rod PQ is fixed in a horizontal position and middle points of PQ and ST are connected by a vertical string. The tension in string is</font></p> <p align="center"> <img style='object-fit:contain' align="bottom" height="134" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0ef42e6377b2e815f4c6e" width="163"/> </p>
Question 283 :
A particle is whirled in a vertical circle of radius <em>l</em> such that on imparting a horizontal velocity when particle is hanging vertically, the particle reaches a maximum height of {tex}\frac{\text{27}l}{\text{16}}{/tex}from its initial bottom position. Then
Question 284 :
A body is in rectilinear motion with an acceleration given by <em>a</em> = 2<em>v</em><sup>3/2</sup>. If particle starts its motion from origin with a velocity of 4 ms<sup>–1</sup>, the position <em>x</em> of the particle at an instant in terms of <em>v</em> can be given as
Question 285 :
A spring balance is adjusted at zero. Elastic collisions are brought about by dropping particles of one gram each on the pan of the balance. They recoil upwards without change is their velocities. If the height of fall of particles is 2 meter and the rate of particle dropping is 100 per seconds, then the reading of the balance is -<br>
Question 286 :
A spherical ball of mass 20kg is stationary at the top of a hill of height 100m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30m and finally rolls down to a horizontal base at a height of 20m above the ground. The velocity attained by the ball is[2005]<br>
Question 287 :
A 500 g ball is released from a height of 4 m. Each time it makes contact with the ground it loses 25% of its energy. Find the KE it possess after 3<sup>rd</sup> hit :<br>
Question 288 : A particle initially at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance <em>h</em> below the highest point. Then <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bfdabfef6349df00fd40"/>
Question 289 :
A person draws water from a 5 m deep well in a bucket of mass 2 kg of capacity 8 litre by a rope of mass 1 kg. What is the total work done by the person? (g = 10 m/s<sup>2</sup>)<br>
Question 290 :
Potential energy (in joule) of a particle of mass 1 kg moving in <em>x</em>-<em>y</em> plane is <em>U</em> = 3<em>x</em> + 4<em>y</em>, here <em>x</em> and <em>y</em> are in meter. If at time <em>t</em> = 0, particle is at rest at point <em>P</em>(6m, 4m). Then
Question 291 : Which of the following is true of the magnitudes of velocity and acceleration, as the ball moves (slip) down the frictionless slope as shown -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7d976e25bd3947928ed754' height='101' width='107' ><br>
Question 292 :
A body of mass m starting from rest moves with acceleration proportional to cube root of its velocity. The instantaneous power delivered to the body is varying with time as
Question 293 :
A 5g bullet was fixed horizontal into a 1.2 kg wooden block resting on a wooden surface. The coefficient of kinetic friction between the block and surface is 0.2. The bullet remained embedded in the block. The block was found to slide 0.23 m along the surface before stopping. Find initial speed of bullet.<br>
Question 294 :
<font>Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be -</font></p>
Question 295 : The system given in figure is released from rest with the spring initially stretched by <em>x</em>. The velocity <em>v</em> of the block after it has dropped a distance <em>x</em>/2 will be<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bfbaf1a5a149feab9913"/>
Question 296 : If the container pictured below is filled with an ideal fluid, which point in the fluid most likely has the greatest pressure -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7d97fb25bd3947928ed889' height='129' width='212' ><br>
Question 297 :
A light spring of length <em>l</em> and rigidity <em>k</em> is placed vertically on a table. A small ball of mass <em>m</em> falls on it from a vertical distance <em>y</em> above its free end. The height <em>h</em> from the surface of the table at which the ball will have the maximum velocity is
Question 298 :
A uniform chain of length <em>L</em> and mass <em>M</em> overhangs a horizontal table with its two third part on the table. The friction coefficient between the table and the chain is <font face="Symbol">µ</font>. The work done by the friction during the period the chain slips off the table is
Question 299 : <font>The linear momentum of a particle varies with time t as :</font></p> <p align="justify"> <font>p = a + bt + ct</font><sup><font>2</font></sup><font> Which of the following statements is correct ?</font></p>
Question 300 : <font>At the instant t = 0 a force F = kt (k is a constant) acts on a small body of mass m resting on a smooth horizontal surface. The time, when body leaves the surface is -</font></p> <p> <img style='object-fit:contain' align="bottom" height="60" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0ef7c75b85f121f54245d" width="112"/> </p>
Question 301 : <font>Power applied to a particle varies with time as </font> </p> <p align="justify"> <font>P = (3t</font><sup><font>2</font></sup><font> - 2t + 1) watts, where t is time in seconds. Then the </font> </p> <p align="justify"> <font>Change in kinetic energy between time t = 2s to t = 4s is-</font></p>
Question 302 : <font>A particle moves in a straight line with its retardation </font> </p> <p align="justify"> <font>proportional to its displacement 'x'. Change in kinetic energy is proportional to -</font></p>
Question 303 :
<font>A ball of mass m collides with a wall with speed v and rebounds on the same line with the same speed. If the mass of the wall is taken as infinite, then the work done by the ball on the wall is:</font></p>
Question 304 : <font>A particle of mass m = 9 × 10</font><sup><font>-31</font></sup><font> kg moving towards the wall of a vessel at a velocity of </font> </p> <p align="justify"> <font>v = 600 ms</font><sup><font>-1</font></sup><font> strikes it at an angle of 60° to the normal and rebounds at the same angle at the same speed. The impulse of the force experienced by the wall during the impact is -</font></p>
Question 305 :
<font>A particle of mass m is moving in a circular path of constant radius r such that radial acceleration a</font><sub><font>r</font></sub><font> = k</font><sup><font>2</font></sup><font>t</font><sup><font>2</font></sup><font>r. Find the power delivered to the particle by the forces acting on it.</font></p>
Question 307 :
<font>A man squatting on the ground gets straight up and stands. The force of reaction of ground on the man during the process is.</font></p>
Question 308 :
<font>A bullet of mass 0.01 kg and travelling at a speed of 500 m/s strikes a block of 2 kg which is suspended by a string of length 5m. The centre of gravity of the block is found to rise a vertical distance of 0.1 m. What is the speed of the bullet after it emerges from the block ?</font></p>
Question 309 :
<font>A man weighing 60 kg climbs up a staircase carrying a load of 20 kg on his head. The stair case has 20 steps each of height 0.2 m. If he takes 10 s to climb, find his power:</font></p>
Question 311 : <font>A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10 N is acting on it in a direction making an angle of </font> <img style='object-fit:contain' align="bottom" height="16" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0f2ace6377b2e815f5707" width="24"/> <font>with the x-axis and displaces it along the x-axis by 4 metres. The work done by the force is </font></p>
Question 312 :
<font>An ice cream has a marked value of 700 kcal. How many kilowatt hour of energy will it deliver to the body as it is digested</font></p>
Question 313 : <font>Coefficient of friction between a tool and grinding wheel is </font><font face="Symbol, serif"><font></font></font><font>.Power developed in watt by the wheel of radius r running at n revolutions per second when tool is pressed to the wheel with F' kgf is </font> </p> <p align="center"> <img style='object-fit:contain' align="bottom" height="118" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0f580e6377b2e815f590d" width="161"/> </p>
Question 314 :
<font>A spring balance is adjusted at zero. Elastic collisions are brought about by dropping particles of one gram each on the pan of the balance. They recoil upwards without change is their velocities. If the height of fall of particles is 2 meter and the rate of particle dropping is 100 per seconds, then the reading of the balance is -</font></p>
Question 315 :
<font>A weightlifter lifts a weight off the ground and holds it up :</font></p>
Question 316 : A man of mass 50 kg is moving up an inclined plane pull a block of mass 25 kg with constant speed 1 m/s. Friction coefficient between block and plane is 0.5. Assuming that man doesn't slips. Power delivered by man -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7d96eef24c9c46dfc10148' height='90' width='120' ><br>
Question 317 :
<font>n small balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will be</font></p>
Question 318 :
<font>A person pushes a block of mass 4 kg up a frictionless inclined plane 10 m long and that makes an angle of 30° with the horizontal. Then the work done is -</font></p>
Question 319 :
A particle is moving along a circular path of radius 6 m with a uniform speed of 8ms<sup> − 1</sup>. The average acceleration when the particle completes one half of the revolution is
Question 320 : From a canon mounted on a wagon at height <em>H</em> from ground, a shell is fired horizontally with a velocity <em>v</em><sub>0</sub> with respect to canon. The canon and wagon has combined mass <em>M</em> and can move freely on the horizontal surface. The horizontal distance between shell and canon when the shell touches the ground is <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd841da6d070c2abf85e"/>
Question 321 :
With what angular velocity should a 20 m long cord be rotated such that tension in it, while reaching the highest point, is zero
Question 322 :
A body starts from rest with uniform acceleration and remains in motion for <em>n</em> seconds. If its final velocity after <em>n</em> second is <em>v</em>, then its displacement in the last two seconds will be
Question 323 :
A car is moving on a horizontal circular road of radius 100 m with a uniform speed 10 ms<sup>-1</sup>. It suddenly accelerates at 1 ms<sup>-2</sup>. The acceleration is
Question 324 :
If a body is projected with an angle θ to the horizontal, then -
Question 325 :
A balloon is moving vertically upward with a velocity of 4 m/s. When it is at a height of <em>h</em>, a stone is dropped from it. If it reaches the ground in 4s, the height of the balloon, when the stone is released, is (<em>g</em> = 9.8 m/s<sup>2</sup>)
Question 326 : If a particle goes from point A to point B in 1 s moving in a semicircle (see Fig.). The magnitude of the average velocity is <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e78bb5f89758f2d4f119' height='121' width='68' >
Question 327 :
A particle is thrown with a speed u at an angle θ to the horizontal. When the particle makes an angle φ with the horizontal, its speed changes to v -
Question 328 :
A stone tied to string is rotated in a vertical circle. The minimum speed with which the string has to be rotated
Question 329 :
If the velocity of a particle is (10 + 2<em>t</em><sup>2</sup>) m/s, then the average acceleration of the particle between 2s and 5s is
Question 330 :
A body is moving from rest under constant acceleration and let <em>S</em><sub>1</sub> be the displacement in the first (<em>p</em> – 1) sec and <em>S</em><sub>2</sub> be the displacement in the first <em>p</em> sec. The displacement in (<em>p</em><sup>2</sup> − <em>p</em> + 1)<sup>th</sup> sec will be
Question 331 :
A particle of mass m is fixed to one end of a light rigid rod of length l and rotated in a vertical circular path about its other end. The minimum speed of the particle at its highest point must be-
Question 332 :
Two bodies are projected vertically upwards from one point with the same initial velocities <em>v</em><sub>0</sub> m/s. The second body is thrown τ s after the first. The two bodies meet after time
Question 333 :
A train starts from station A with uniform acceleration {tex}a_{1}{/tex} for some distance and then goes with uniform retardation {tex}a_{2}{/tex} for some more distance to come to rest at station B. The distance between A and B is 4 km and the train takes 4 hours to complete this journey. If acceleration and retardation are in {tex}km/hour^{2}{/tex}, then
Question 334 :
A projectile is fired at 30<sup>o</sup> with momentum p. Neglecting friction, the change in kinetic energy when it returns to the ground will be
Question 335 :
A man can row a boat with speed 4 km/hr in still water. If the velocity of water in river is 3 km/hr. The time taken to reach just opposite end is (river width = 500 m)
Question 336 :
A body is thrown with the velocity {tex} v _ { 0 } {/tex} at an angle {tex} \alpha {/tex} with the horizontal. If the body remains in air for the time {tex} t = 4 s {/tex} , the maximum height reached by the body will be
Question 337 :
Two bodies are projected with the same velocity. If one is projected at an angle of 30<sup>o</sup> and the other at an angle of 60<sup>o</sup> to the horizontal, the ratio of the maximum heights reached is
Question 339 :
The velocity of a particle moving along the <em>x</em>–axis is given by <em>v</em> = <em>x</em><sup>3</sup> – 6<em>x</em><sup>2</sup> + 12 where <em>v</em> is in m/s and <em>x</em> is in <em>m</em>. Acceleration of the particle when it is passing through the point <em>x</em> = 4 <em>m</em> will be
Question 340 :
The ratio of angular velocity of rotation of minute hand of a clock with the angular velocity of rotation of the earth about its own axis is
Question 341 :
Theequationofmotionofaprojectileis {tex} y = 12 x - \frac { 3 } { 4 } x ^ { 2 } {/tex} . Given that {tex} g = 10 \mathrm { ms } ^ { - 2 } , {/tex} what is the range of the projectile?
Question 342 :
A stone is allowed to fall from the top of a tower and cover half the height of the tower in the last second of its journey. The time taken by the stone to reach the foot of the tower is
Question 343 :
The initial velocity of a particle moving along a straight line is 12{tex} \mathrm { ms } ^ { - 1 } {/tex} and its retardation is 3{tex} \mathrm { ms } ^ { - 2 } {/tex}. The distance moved by the particle in the fourth second of its motion is
Question 344 : Blocks <em>A</em> and <em>C</em> start from rest and move as shown with acceleration <em>a</em><sub><em>A</em></sub> = 12<em>t</em> m/s<sup>2</sup> and <em>a</em><sub><em>C</em></sub>=3 m/s<sup>2</sup>. Here <em>t</em> is in seconds. The time when block <em>B</em> again comes to rest is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd6b1da6d070c2abf840"/>
Question 345 :
A particle is projected vertically upwards from a point <em>A</em> on the ground. It takes time <em>t</em><sub>1</sub> to reach a point <em>B</em>, but it still continues to move up. If it takes further <em>t</em><sub>2</sub> time to reach the ground from point <em>B</em>. Then height of point <em>B</em> from the ground is
Question 346 :
A cricketer can throw a ball to a maximum horizontal distance of 100{tex} \mathrm { m } {/tex} . How much high above the ground can the cricketer throw the same ball?
Question 347 :
A boat, which has a speed of {tex}5 \mathrm { km } / \mathrm { h } {/tex} in still water, crosses a river of width {tex}1 \mathrm { km } {/tex} along the shortest possible path in 15 minutes. The velocity of the river water in kilometers per hour is
Question 348 :
The position of an object moving along {tex} x {/tex} -axis is given by {tex} x = a t ^ { 3 } + b t + 3 , {/tex} where {tex} x {/tex} is in metres and {tex} t {/tex} in seconds. If velocity at {tex} t = 1 {/tex} s and {tex} t = 4 {/tex} s is {tex}0.3 \mathrm { m } / \mathrm { s } {/tex} and {tex} 27.3{tex} \mathrm { m } / \mathrm { s } {/tex} respectively, the value of {tex} a {/tex} and {tex} b {/tex} will be
Question 349 :
The equation of trajectory of an oblique projectile is {tex} y = x - \frac { 1 } { 2 } x ^ { 2 } . {/tex} The time of flight of projectile will be
Question 350 :
A particle is projected with a velocity {tex} u , {/tex} at an angle {tex} \alpha , {/tex} with the horizontal. Time at which its vertical com- - ponent of velocity becomes half of its net speed at the highest point will be
Question 351 : A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point <em>C</em> starting from <em>A</em>. He swims with a speed of<br/> 5 km/hr with respect to river flow at angle θ as shown. If<br/> <em>AB</em> = <em>BC</em> = 400 m, the value of θ is <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bda21da6d070c2abf884"/>
Question 352 :
A particle moves along {tex} x {/tex} -axis as {tex} x = 4 ( t - 2 ) + a ( t - 2 ) ^ { 2 } {/tex} Which of the following is true?
Question 353 :
A particle is thrown with a speed of {tex}12 \mathrm { m } / \mathrm { s } {/tex} at an angle {tex} 60 ^ { \circ } {/tex} with the horizontal. The time interval between the moments when its speed is {tex} 10\mathrm { m } / \mathrm { s } {/tex} is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 354 :
A ball is thrown vertically upwards from the ground. It crosses a point at the height of {tex}25{tex} \mathrm { m } {/tex} twice at an interval of {tex} 4 \mathrm { s } . {/tex} The ball was thrown with the velocity of {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 355 :
A body starts from rest and travels with uniform acceleration such that it covers 8 m during the {tex} 2 ^ { \text { nd } } {/tex} second. During the 5th second it would travel
Question 356 :
A man holds an umbrella at {tex} 30 ^ { \circ } {/tex} with the vertical to keep himself dry. He, then, runs at a speed of 10{tex} \mathrm { ms } ^ { - 1 } {/tex} and finds the rain drops to be hitting vertically. Speed of the rain drops with respect to the running man and with respect to earth are
Question 357 :
A particle starts moving from the position of rest under a constant acceleration. It travels a distance {tex} x {/tex} in the first 10{tex} \mathrm { s } {/tex} and distance {tex} y {/tex} in the next {tex} 10 \mathrm { s } , {/tex} then
Question 358 :
An aeroplane is rising vertically with acceleration <em>f</em>. Two stones are dropped from it at an interval of time <em>t</em>. The distance between them at time <em>t′</em> after the second stone is dropped will be
Question 359 : A marble rolls down from top of a staircase with constant horizontal velocity u.If each step is y metre high and x metre wide, the marble just hits the edge of the nth step when n =<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e5b4b5f89758f2d4ef54' height='126' width='147' >
Question 360 :
Six particles situated at the corners of a regular hexagon of side a move at a constant speed <em>v</em>. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other
Question 361 : A particle is projected with a speed 10 <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e6e0491ec9580069801a' height='21' width='23' > m/s and at angle 45<sup>0</sup> with the horizontal. The rate of change of speed with respect to time at t = 1 s is (g = 10 m/s<sup>2</sup>)
Question 362 :
A projectile is thrown horizontally from top of a building of height {tex}10 \mathrm { m } {/tex} with certain speed {tex} ( u ) {/tex} . At the same time another projectile is thrown from ground 10{tex} \mathrm { m } {/tex} away from the building with equal speed {tex} ( u ) {/tex} on the same vertical plane. If they collide after {tex} 2 s , {/tex} then choose the correct options.
Question 363 :
One body is dropped, while a second body is thrown downward with an initial velocity of 1{tex} \mathrm { ms } ^ { - 1 } {/tex} simultaneously. The separation between these is 1.8{tex} \mathrm { m } {/tex} after a time
Question 364 :
In a harbour, wind is blowing at the speed of {tex}72 \mathrm { km } / \mathrm { h } {/tex} and the flag on the mast of a boat anchored in the harbour flutters along the {tex} \mathrm { N } - \mathrm { E } {/tex} direction. If the boat starts moving at a speed of {tex}51 \mathrm { km } / \mathrm { h } {/tex} to the north, what is the direction of the flag on the mast of the boat?
Question 365 :
{tex}\mathrm {Assertion} \quad {/tex} :Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection the downward direction with the same speed.<br> {tex}\mathrm {Reason} \quad {/tex} :With the maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.
Question 366 :
{tex} \begin{array} { l l } { \text { Assertion } } & {: \text { A body can have acceleration even if its velocity is } } \\ { } & { \text { zero at a given instant of time. } } \\ { \text { Reason } } & {: \text { A body is momentarily at rest when it reverses its } } \\ { } & { \text { direction of motion. } } \end{array} {/tex}
Question 367 :
A stone is dropped into water from a bridge {tex} 44.1 \mathrm { m } {/tex} above the water. Another stone is thrown vertically downward 1 sec later. Both strike the water simultaneously. What was the initial speed of the second stone
Question 368 :
Consider a car moving on a straight road with a speed of $100m/s$. The distance at which car can be stopped (${\mu}_{k}=0.5$)
Question 369 :
The displacement of a particle moving in a straight line is described by the relation, $s=6+12t-2{ t }^{ 2 }$. Here $'s'$ is in metre and $'t'$ is in second. The distance covered by particle in first $5\ sec$ is:
Question 370 :
The compass needle of the airplane shows it is heading due North and speedometer indicates a velocity 240 kmh<sup>-1</sup>. Wind is blowing 100 kmh<sup>-1</sup> due east. Find the velocity of airplane with respect to earth.
Question 371 :
Which of the following statement is true if a body moves in a semicircular track whose radius is R:
(a) 2R is the displacement of the body
(b) {tex} \pi {/tex}R is the distance traveled by the body
(c) Both (a) and (b) are correct
(d) None of the above
Question 372 : A 2m wide truck is moving with a uniform speed {tex}v_{0} = 8 m/s{/tex} along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4m away from him. The minimum value of v so that he can cross the road safely is <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5804db40fda93533ee5b47" />
Question 373 :
A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which a height {tex} 4 h{/tex}. The two stones cross each other after time
Question 374 : A given shaped glass tube having uniform area of cross - section is filled with water and is mounted on a rotatable shaft as shown in fig. If the tube is rotated with a constant angular velocity ω, then <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e5dc491ec95800697f20' height='167' width='219' >
Question 375 :
A wall clock has a 5 cm long minute hand. The average velocity of the tip of the hand reaching 0600 hrs. to 1830 hrs. is
Question 376 :
A ball is thrown from the ground to clear a wall <b>3 m</b> high at a distance of <b>6 m</b> and falls <b>18 m</b> away from the wall, the angle of projection of ball is
Question 377 :
Two trains {tex} A {/tex} and {tex} B {/tex} are moving on same track in opposite direction with velocity {tex}25 \mathrm { m } / \mathrm { s } {/tex} and {tex}15 \mathrm { m } / \mathrm { s } {/tex} respectively. When separation between them becomes {tex} 225 \mathrm { m } , {/tex} drivers of both the trains apply brakes producing uniform retardation in train {tex} A {/tex} while retardation of train {tex} B {/tex} increases linearly with time at the rate of {tex} 0.3 \mathrm { m } / \mathrm { s } ^ { 3 } . {/tex} The minimum retardation of train {tex} A {/tex} to avoid collision will be
Question 378 :
Two trains one of length {tex} 100 \mathrm { m } {/tex} and another of length {tex} 125 \mathrm { m } , {/tex} are moving in mutually opposite directions along parallel lines, meet each other, each with speed {tex} 10 \mathrm { m } / \mathrm { s } {/tex}. If their acceleration are {tex} 0.3 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} and {tex} 0.2 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} respectively, then the time they take to pass each other will be
Question 379 :
A man standing on the roof of a house of height {tex} h {/tex} throws one particle vertically downwards and another particle horizontally with the same velocity {tex} u . {/tex} The ratio of their velocities when they reach the earth's surface will be
Question 380 :
Three particles {tex} A , B {/tex} and {tex} C {/tex} are thrown from the top of a tower with the same speed. {tex} A {/tex} is thrown up, {tex} B {/tex} is thrown down and {tex} C {/tex} is horizontally. They hit the ground with speeds {tex} V _ { A } , V _ { B } {/tex} and {tex} V _ { C } {/tex}<br>respectively.<br>
Question 381 :
Rain is falling vertically with a speed of {tex}30 ms^{-1}{/tex}. A woman rides a bicycle at a speed of {tex}10 ms^{-1}{/tex} in the north to south direction. What is the direction in which she should hold her umbrella?
Question 382 :
A particle starts from rest and moves with uniform acceleration. If covers a displacement of $y^{2}-x^{2}$ in the first $10\ sec$ and $y^{2}+x^{2}$ in the next first $10\ sec$, then
Question 383 :
A constant force acts on a body of mass $0.9 kg $ at rest for $10 s$ . If the body moves a distance of $250 m,$ the magnitude of the force is :
Question 384 :
A light beam is being reflected by using two mirrors, as in a periscope used in submarines. If one of the mirrors rotates by an angle {tex} \theta , {/tex} the reflected light will deviate from its original path by the angle
Question 385 :
An electromagnetic wave going through vacuum is described by {tex} E = E _ { 0 } \sin ( kx - \omega t ) ; \quad B = B _ { 0 } \sin ( kx- \omega t ) . {/tex} Which of the following equation is true
Question 386 :
Pick out the longest wavelength from the following types of radiations
Question 387 :
The phase difference between incident wave and reflected wave is {tex} 180 ^ { \circ } {/tex} when light ray
Question 388 :
In a Young's double slit experiment, the slit separation is 1 mm and the screen is 1 m from the slit. For a monochromatic light of wavelength 500 nm, the distance of 3rd minima from the central maxima is
Question 390 :
A calcite crystal is placed over a dot on a piece of paper and rotated, on seeing through the calcite one will be see
Question 391 : A ray of light passes through four transparent media with refractive indices {tex} \mu _ { 1 } , \mu _ { 2 } , \mu _ { 3 } , {/tex} and {tex} \mu _ { 4 } {/tex} as shown in the Fig. The surfaces of all media are parallel. If the emergent ray {tex} C D {/tex} is parallel to the incident ray {tex} A B , {/tex} then<br><img src="https://s3.ap-south-1.amazonaws.com/me-p/5eee0b0d97c31b19a3d282f0.jpg" />
Question 392 :
Two thin lenses of focal lengths {tex} f _ { 1 } {/tex} and {tex} f _ { 2 } {/tex} are in contact and coaxial. The combination is equivalent to a single lens of power<br>
Question 393 :
In an electromagnetic wave, the electric and magnetising fields are {tex} 100 \mathrm { V } m ^ { - 1 } {/tex} and {tex} 0.265 A m ^ { - 1 } . {/tex} The maximum energy flow is
Question 394 :
In Young's double slit experiment, the width of one slit is double that of the other. The ratio of intensity of a bright band to that of a dark band in the interference pattern will be
Question 395 :
Consider the following statements in case of Young's double slite experiment.<br>(1) A site S is necessary if we use an ordinary extended source of light.<br>(2) A slit S is not needed if we use an ordinary but well collimated beam of light.<br>(3) A slit S is not needed if we use a spatially coherent source of light.<br>Which of the above statement are correct?
Question 396 :
Colours of thin films result from<br>On a rainy day, a small oil film on water show brilliant colours. This is due to<br>
Question 398 :
A thin plano-convex lens acts like a concave mirror of focal length {tex} 0.2 ~ m {/tex} when silvered from its plane surface. The refractive index of the material of the lens is {tex} 1.5 . {/tex} The radius of curvature of the convex surface of the lens will be
Question 399 :
A bulb is placed at a depth of {tex}2\sqrt{7}{/tex} m in water and a floating opaque disc is placed over the bulb so that the bulb is not visible from the surface. The radius of the disc should be at least (<font face="Symbol">µ</font><sub>water</sub> = 4/3)
Question 400 :
A concave mirror gives an image three times as large as the object placed at 20cm from it. For the image to be real, the focal length should be
Question 401 :
Plane polarised light is passed through a polaroid. On viewing through the polaroid we find that when the polariod is given one complete rotation about the direction of the light, one of the following is observed<br>
Question 402 : Two convex lenses placed in contact form the image of a distant object at <em>P</em>. If the lens <em>B</em> is moved to the right, the image will <br> <img style="max-width:240px;" src="5f16c82d4bec8070e4e152a8"/>
Question 403 :
What will be the angle of diffracting for the first minimum due to Fraunhoffer diffraction with sources of light of wave length {tex} 550 \mathrm { nm } {/tex} and slit of width {tex} 0.55 \mathrm { mm } {/tex}
Question 404 :
Two plane mirrors are at {tex} 45 ^ { \circ } {/tex} to each other. If an object is placed between them, then the number of images will be
Question 406 :
Light of wavelength {tex} \lambda = 5000 A ^{\circ}{/tex} falls normally on a narrow slit. A screen placed at a distance of 1 {tex} m {/tex} from the slit and perpendicular to the direction of light. The first minima of the diffraction pattern is situated at {tex} 5 \mathrm { mm } {/tex} from the centre of central maximum. The width of the slit is
Question 407 :
A man having height {tex} 6\ \mathrm { m } {/tex}. He observes image of {tex} 2\ \mathrm { m } {/tex} height erect, then mirror used is
Question 409 :
A thin sheet of glass (<font face="Symbol">µ</font>=1.5) of thickness 6 microns introduced in the path of one of interfering beams of a double slit experiment shifts the central fringes to a position previously occupied by fifth bright fringe. Then the wavelength of the light used is
Question 410 :
A combination of two thin convex lenses of focal length {tex} 0.3 \mathrm { m } {/tex} and 0.1 {tex} m {/tex} will have minimum spherical and chromatic aberrations if the distance between them is<br>
Question 411 :
A beam of natural light falls on a system of 6 polaroids, which are arranged in succession such that each polaroid is turned through {tex} 30 ^ { \circ } {/tex} with respect to the preceding one. The percentage of incident intensity that passes through the system will be
Question 412 :
A ray of light is incident on the plane mirror at rest. The mirror starts turning at a uniform angular acceleration of 2π rad s<sup>–2</sup>. The reflected ray, at the end of {tex}\frac{1}{4}{/tex}s must have turned through
Question 413 :
A planet is observed by an astronomical refracting telescope having and objective of focal length 16 m and an eye piece of focal length 2 cm then :
Question 414 :
Two point white dots are {tex} 1\,\mathrm { mm } {/tex} apart on a black paper. They are viewed by eye of pupil diameter {tex} 3\,\mathrm { mm } {/tex} . Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light = {tex} 500 \mathrm { nm } {/tex}]
Question 415 :
In a double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then in the interference pattern
Question 416 :
Light wave enters from medium 1 to medium 2. Its velocity in 2<sup>nd</sup> medium is double from 1<sup>st</sup>. For total internal reflection the angle of incidence must be greater than
Question 417 :
A rocket is going towards moon with a speed {tex} v {/tex}. The astronaut in the rocket sends signals of frequency {tex} v {/tex} towards the moon and receives them back on reflection from the moon. What will be the frequency of the signal received by the astronaut (Take {tex}v << c {/tex})
Question 418 : Two coherent sources <em>S</em><sub>1</sub> and <em>S</em><sub>2</sub> are emitting light of wavelength 5000 Å are placed at 0.1 mm apart, as shown in the figure. A detector is moved along a line perpendicular to S<sub>1</sub>S<sub>2</sub> and passing through S<sub>1</sub> .The position of farthest maxima from <em>S</em><sub>1</sub> is approximately at a distance of <br> <img style="max-width:240px;" src="5f16c83ebfef6349df01002b"/>
Question 419 : In the figure is shown Young's double slit experiment.{tex} Q {/tex} is the position of the first bright fringe on the right side of {tex} O {/tex}. {tex} P {/tex} is the II fringe on the other side, as measured from {tex} Q {/tex}. If the wavelength of the light used is {tex} 6000 \times 10 ^ { - 10 } \mathrm { m } {/tex}, then {tex} S _ { 1 } B {/tex} will be equal to<br><br><img src="5dc3ac2de18860128132dc69"><br>
Question 420 :
In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude {tex} A {/tex} and wavelength {tex}\lambda{/tex}. In another experiment with the same set up the two slits are of equal amplitude {tex} A {/tex} and wavelength {tex}\lambda{/tex} but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is<br>
Question 421 :
The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre is
Question 422 :
In a single slit diffraction of light of wavelength {tex} \lambda {/tex} by a slit of width {tex} e {/tex}, the size of the central maximum on a screen at a distance {tex} b {/tex} is
Question 423 :
In the Young's double slit experiment with sodium light. The slits are {tex} 0.589 \mathrm { m } {/tex} a part. The angular separation of the third maximum from the central maximum will be (given {tex} \lambda = 589 \mathrm { mm } {/tex} )
Question 424 : A light ray falls on a square slab at an angle {tex} 45 ^ { \circ } . {/tex} What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?<br><img src="5d5bb2485637834a588986e3"><br>
Question 425 :
In Young's double slit experiment, a mica slit of thickness {tex} t {/tex} and refractive index {tex} \mu {/tex} is introduced in the ray from the first source {tex} S {/tex}. By how much distance the fringes pattern will be displaced
Question 426 :
A spherical surface of radius of curvature {tex} R {/tex} separates air (refractive index 1.0{tex} ) {/tex} from glass (refractive index 1.5.) The centre of curvature is in the glass. A point object {tex} P {/tex} placed in air is found to have a real image {tex} Q {/tex} in the glass. The line {tex} P Q {/tex} cuts the surface at a point {tex} O {/tex}, and {tex} P O = O Q . {/tex} The distance {tex} P O {/tex} is equal to
Question 427 : Light is incident normally on face {tex} A B {/tex} of a prism as shown in Fig. A liquid of refractive index {tex} \mu {/tex} is placed on face {tex} A C {/tex} of the prism. The prism is made of glass of refractive index {tex} 3 / 2 . {/tex} The limits of {tex} \mu {/tex} for which total internal reflection cannot takes place on face {tex} A C {/tex} is<br><br> <img src='5e8acd07fe2ff92479fb1880' class="uploaded-image" />
Question 429 :
For skywave propagation of a {tex} 10 \mathrm { MHz } {/tex} signal, what should be the minimum electron density in ionosphere
Question 430 : Two plane mirrors {tex} A {/tex} and {tex} B {/tex} are aligned parallel to each other as shown in Fig. A light ray is incident at an angle of {tex} 30 ^ { \circ } {/tex} at a point just inside one end of {tex} A {/tex}. The plane of incidence coincides with the plane of the Fig. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is<br> <img src='5e8acc7d18534f243179e3b5' class="uploaded-image" />
Question 431 :
In a Young's experiment, two coherent sources are placed 0.90{tex} \mathrm { mm } {/tex} apart and the fringes are observed 1{tex} \mathrm { m } {/tex} away. If it produces the second dark fringe at a distance of 1{tex} \mathrm { mm } {/tex} from the central fringe, the wavelength of monochromatic light used would be
Question 432 :
If {tex} I _ { 0 } {/tex} is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit<br>width is doubled<br>
Question 433 :
Assertion: Light of different colors travel with different speeds in vacuum.
Reason: Speed of light depends on medium.
Question 434 :
The refractive index of a certain glass is $$1.5$$ for light where wavelength in vacuum is $$6000 A^o V$$ The wavelength of this light when it passes through the glass is ___________.
Question 435 :
If refractive index of a slab varies as $$m = 1 + x^2$$ is measured from one end, then optical path length of a slab of thickness 1 m is
Question 436 :
In vacuum, to travel distance 'd', light takes time 't' and in medium to travel distance $$'5d'$$, it takes time 'T'. The critical angle of the medium is.<br>
Question 437 :
Air has refractive index $$1.0003$$. Find the thickness of air column which will contain one more wavelength of yellow light of $$6000$$ $$A^0$$ than in same thickness of vacuum.
Question 438 :
The angle which the __________ makes with the normal at the point of incidence is called angle of incidence.<br/>
Question 439 :
A water film is formed on a glass-block. A light ray is incident on water film from air at an angle of $$\displaystyle { 60 }^{ \circ }$$ with the normal. The angle of incidence on glass slab is<br>($$\displaystyle { \mu }_{ g } = 1.5,{ \mu }_{ w } = \frac { 4 }{ 3 } $$)
Question 440 :
The refractive indices of four substances W, X, Y, Z are $$1.20, 1.77, 1.36, 1.50$$ respectively. When light passes from air into these materials, it refracts maximum in<br/>
