Question 1 :
If a man of $30$ kilograms climbs stairs in $4$ seconds when height of stairs is $5$ meters, power output produced will be:<br/>
Question 4 :
Which of the following can be used to express energy? Symbols have their usual meanings for the units of physical quantities.<br/>(i) Wh   (ii) VC    (iii) VAs$^2$  (iv)  A$^2\Omega$s<br/>
Question 5 :
How much energy does a 60W electric bulbtransfer in 1 minute?
Question 7 :
Assertion: Kilowatt Hour is the unit of electric power
Reason: KWH is a commercial unit used for expressing consumed electrical energy.
Question 8 :
An X-ray tube is run at 50 kV.. the current flowing in it is 20 mA. The power of the tube is:
Question 11 :
A car of mass $2,000 kg$ is lifted up a distance of $30 m$ by a crane in $1\ minute$. A second crane does the same job in $2\ minutes$.The power supplied by first crane is:
Question 14 :
A man can lift a block of mass of 50 kg up to a height of 2 m in 2 seconds. Calculate the power developed by the man to lift the block.
Question 17 :
An engine lifts a load of $1200\ N$ from a depth of $200 \ m$ in 4  minutes bringing it to the ground level. The power developed by the engine is:
Question 19 :
A man weighing 600 N carries a load of 150 N up the stairs 6 m high in 15 seconds. His power will be:
Question 20 :
A house uses 7 tubelight of 50 W each for 5 hours a day. The electrical energy consumption for one day is:
Question 21 :
What does the slope of work-time curve at any instant represent?
Question 23 :
A machine gun fires $420$ bullets $per\ minute$. The velocity of each of the bullets is $300 m s^{-1}$ and the mass of each bullet is $1 gm$. The power of machine gun is:
Question 28 :
A juggler throws continuously balls at the rate ofthree in each second each with a velocity of $10\ ms^{-1}$. If the mass of each ball is $0.05\ kg$ hispower is:
Question 32 :
Mohan uses one television of $100$ W for $10$ hrs how much energy is consumed by Mohan.
Question 33 :
An engine develops 10 kW of power. How much time will it take to lift a mass of 200kg to a height of 40m (g = 10 $ms^{-2}$)?
Question 34 :
Six electric appliances of 100 watts each are used for 6 hours. The electrical energy consumed is:
Question 35 :
If the power of the motor of a water pump is $3\ kW$, then the volume of water that can be liftedto a height of $10\ m$ in one minute by the pump is ($g= 10 \ m /s^{2}$) :
Question 38 :
Fill in the blanks:One kilowatt is equal to ________ horse power.
Question 39 :
A car of mass $2,000 kg$ is lifted up a distance of $30 m$ by a crane in $1\ minute$. A second crane does the same job in $2\ minutes$. The power supplied by second crane is:
Question 41 :
A machine gun fires $240$ bullets $per\ minute$ with a certain velocity. If the mass of each bullet is $10 gm$ and the power of the gun is $7.2 kW$, the velocity with which each bullet is fired must be:
Question 44 :
In our household applications, commercial unit of electricity is used. One unit is equal to:
Question 45 :
Which of the following must be known in order to determine the power output of an automobile? <br>
Question 46 :
If the force applied is $F$ and the velocity gained is $v$, then the power developed is:
Question 47 :
The power of a crane is 6.25 kW. How much mass of coal it can lift in 1 hour from a mine of 100 m depth? The efficiency of the crane is 80% and $g = 10 \ m s^{-2}$.
Question 48 :
1 kilowatt-hour is the amount of .... by 1000 watt electric appliance when it operates for one hour.
Question 51 :
A crane can lift up $10000\ kg$ of coal in $1\ hour$ from a mine of $180\ m$ depth. If the efficiency of the crane is $80 \%$, its input power must be:  [Take : $g = 10  \ ms^{-2}$]
Question 52 : <p>The distance of two planets from the Sun are ${ 10 }^{ 13}$ and ${ 10 }^{ 12 }$ m, respectively. The ratio of time periods of thesetwo planets is</p>
Question 53 :
A particle is displaced from a position $(2\hat {i}-\hat {j}+\hat {k})$ metre to another position $(3\hat {i}+2\hat {j}-2\hat {k})$ metre under the action of force $(2\hat {i}+\hat {j}-\hat {k})\ N$. Work done by the force is
Question 54 :
A satellite is fired from the surface of the moon of mass $M$ and radius $R$ with speed $\displaystyle v_{0}\:\:  at\: \: 30^{\circ}$ with the vertical The satellite reaches a maximum distance of $\displaystyle \frac{5R}{2}$ from the center of the moon The value of $\displaystyle v_{0}$ is
Question 56 :
A person brings a mass of $1 kg$ from infinity to a point A. Initially the mass was at rest but it moves with a speed of $2 m/s$ as it reaches A. The work done by the person on the mass is $3 J.$ The potential of A is.
Question 57 :
If voltage across a bulb rated $220$V-$100$W drops by $2.5\%$ of its rated value, the percentage of the rated value by which the power would decrease is
Question 58 :
A man raises a box of mass $50kg$ to a height of $2m$ in $2$ minutes, while another man raises the same box to the same height in $5$ minutes. Ratio of the power developed by them:
Question 59 :
If Rahul has done the same amount of work in less time compared to Rohan then :<br/>
Question 60 :
The Jog falls in Karnataka state are nearly $20$ m high. $2000$ tonnes of water falls from it in a minute. Calculate the equivalent power if all this energy can be utilized $(g=10 \:m \:s^{-2})$:<br/>
Question 61 :
Calculate the power of an engine required to lift $10^{5}kg$ of coal per hour from a mine $360m$ deep. Consider $g=10m{s}^{-2}$.
Question 62 :
A lamp rated $20w$ and an electric iron rated $50w$ are used for $2$ hour everyday. Calculate the total energy consumed in $20 days.$
Question 63 :
An engine lifts $2250$ litres of water per minute from a well $20 m$ deep. If $25$ % energy of the engine is wasted, the power to be given to the engine must be (Take $g=9.8 \ m/s^2$)
Question 64 :
A crane is used to lift $10000 \ kg$ of coal from a mine $100 \ m$ deep. If the time taken by the crane is $1\  hr$, then find the power of the crane, assuming the  efficiency of the  crane  to  be $80$%. <br/>($g = 9.8\  m/s^2$) :
Question 65 :
Gravitational potential difference between surface of a planet and a point situated at a height of $20m$ above its surface is $2 joule/kg$. If gravitational fieldis uniform, then the work done in taking a $5kg$ bodyof height $4$ meter above surface will be :-
Question 67 :
A car of mass 2,000 kg is lifted up a distance of 30 m by a crane in 1 minute. A second crane does the same job in 2 minutes. The power supplied by first crane is :<br/>
Question 68 :
If $g$ is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass $m$ raised from the earth's surface to a height equal to the radius $R$ of the earth is
Question 69 :
The work done by the heart is $1J$ per beat. Calculate the power of the heart if it beats $72$ times in a minute.
Question 70 :
The potential energy of a body of mass $m$ isgiven by $U=px+qy+rz$. The magnitude of theacceleration of the body will be<br>
Question 71 :
A car of mass 2,000 kg is lifted up a distance of 30 m by a crane in 1 minute. A second crane does the same job in 2 minutes. The power supplied by second crane is :<br/>
Question 72 :
The gravitaional field in a region due to a certainmass distribution is given by $\overrightarrow{E}= \left (4\hat{i}-3\hat{j} \right )\ \text{N/kg}.$ The work done by the field in moving a particle ofmass $2\ \text{kg}$ from $(2\ \text{m,} 1\ \text{m})$ to $\left ( \dfrac{2}{3}\ \text{m,}\ 2\ \text{m} \right )$ along theline $3x+4y=10$ is<br>
Question 73 :
How much power must a motor supply to pull a $1000 kg$ box along a horizontal surface if the box is to move at a constant rate of $2 {m}/{s}$, if the coefficient of kinetic friction between the box and the surface is $\mu = 0.3$?
Question 74 :
Assertion: Power of a engine depends on mass, angular speed, torque and angular momentum, then the formula of power is not derived with the help of dimensional method.
Reason: In mechanics, if a particularly quantity depends on more than three quantities, then we can not drive the formula of the quantity by the help of dimensional method.
Question 76 :
Two men with weights in the ratio $4 : 3$ run up a staircase in time in the ratio $12 : 11$. The ratio of power of the first to that of second is:
Question 77 :
Three particles of mass $M$ each are placed at corners of an equilateral triangle of side $'d'$ if the sides are increased to $'2d'$ then :
Question 79 :
A force F acting on a particle depends upon displacement x as F $\propto $ $x^3$. The power delivered by force depends upon x as
Question 80 :
A pump is used to lift $500\ kg$ of water from a depth of $80\ m$ in $10\ s$. Calculate the power rating of the pump if its efficiency is $40\%$ :<br/>
Question 81 :
Assertion: A crane P lifts a car up to a certain height in 1 min. Another crane Q lifts the same car up to the same height in 2 min. Then crane P consumes two times more fuel than crane Q.
Reason: Crane P supplies two times more power than crane Q.
Question 82 :
A man weighing 60 kg lifts a body of 15 kg tothe top of a building 10 m high in 3 minutes. Thepower of man is.
Question 83 :
Let $V_G$ and $E_G$ denote gravitational potential and field respectively, the it is possible to have
Question 84 :
The amount of energy consumed by a 10hp water pump in 30 minutes to lift the water to overhead tank is :<br/>
Question 85 :
Helios-B spacecraft had a speed of $71$ km/s when it was $4.3 \times 10^7 km$ from the sun. Its orbit is
Question 86 :
An ox can apply a maximum force of $1000N$. It is taking part in a cart race and is able to pull the cart at a constant speed of $30ms^{-1}$ while making its best effort. Calculate the power developed by the ox.
Question 88 :
If a satellite is moved from one stable circularorbit to a farther stable circular orbit, then thefollowing quantity increases<br>
Question 91 :
How long will it take to perform $440 J$ of work at the rate of $11 W$?
Question 92 :
The potential energy of a satellite of mass $m$ and revolving at a height $R_e$ above the surface of earth where $R_e=$ radius of earth, is
Question 93 :
The velocity of a train is increased from $10\ ms^{-1}$to $25 \ ms^{-1}$ in $2$ minutes due to the application of some force by its engine developing an average power of $525\ kW$. Neglecting frictional forces, the mass of the train must be
Question 94 :
A crane can lift a box of 600 kg mass to a height of 20 m in 2 minutes. Calculate the power at which the crane is operating ?<br/>
Question 95 :
What average horsepower is developed by a an $80kg$ man while climbing in $10s$ flight of stair that rises $6m$ vertically?
Question 96 :
The heart takes and discharges $7500$ $l$ of blood in a day. Density of blood $= 1.05 \times 10^3 kg  m^{-3}$. If on an average it takes to a height of $1.6\  m$. Find the power of the heart pump.
Question 97 :
A pump motor is used to deliver water at a certain rate from a given pipe. To obtain thrice as much water from the same pipe in the same time, power of the motor has to be increased to:
Question 98 :
When we pay for our electricity bill, we are paying for the ____________.
Question 99 :
A pendulum of mass $1\ kg$and length $l = 1\,{\text{m}}$ is released from rest at angle $\theta = \,{60^ \circ }$ . The power delivered by all the forces acting on the bob at the angle $\theta = \,{30^ \circ }$ will be $\left( {g = 10\,{\text{m/}}{{\text{s}}^2}} \right)$.
Question 100 :
Kilowatt is the unit of electrical _______ but kilowatt-hour is the unit of electrical _______.<br/>
Question 101 :
The power of engine of a car of mass 12  kg is 25 kW. The minimum time required to reach a velocity of 90 km/h by the car after starting from rest is:
Question 102 :
The percentage change in the acceleration of the earth towards the Sun from a total eclipse of the Sun to the point where the Moon is on a side of earth directly opposite to the Sun is<br>
Question 103 :
Two uniform solid spheres of equal radii R, but mass M and 4M have a centre to centre separation 6 R, the two spheres are held fixed on a horizontal floor. A projectile of mass m is projected from the surface of the sphere of mass M directly towards the centre of the second sphere. Obtain an expression for the minimum speed v of the projectile so that it reaches the surface of the second sphere<br/>
Question 104 :
What is the velocity of proton when it reaches back $5 m$ away?
Question 105 :
A particle of mass $m$ moves in a circular path of radius $r$ , under the action of force which delivers it constant power $p$ and increases its speed. The angular acceleration of particle at time $(t)$ is proportional
Question 106 :
A tunnel is dug along a diameter of the earth. If ${ M }_{ e }$ and ${ R }_{ e }$ are the mass and radius, respectively, of the earth, then the force on a particle of mass ${ m }$ placed in the tunnel at a distance ${ r }$ from the centre is :
Question 107 :
What is the equation of motion for the rocket, if $m$ is the mass of the rocket at a givenmoment, $\vec{w}$ is its acceleration, and $\vec{F}$ is the external force.
Question 108 :
A cavity of radius $R/2$ is made inside a solid sphere of radius $R$. The centre of the cavity is located at a distance $R/2$ from the centre of the sphere. The gravitational force on a particle of mass $m$ at a distance $R/2$ from the centre of the sphere on the line joining both the centres of the sphere and the cavity is (opposite to the centre of the cavity)<br>[Here $g=(GM)/{R}^{2}$, where $M$ is the mass of the sphere]<br>
Question 109 :
Consider two solid uniform spherical objects of the same density $\rho$. One has radius $R$ and the other has radius $2R$. They are in outer space where the gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?<br>
Question 110 :
A body is thrown from the surface of the earth with velocity $\sqrt{(g{R}_{e})/2}$, where ${R}_{e}$ is the radius of the earth at some angle from teh vertical. If the maximum height reached by the body is ${R}_{e}/4$, then the angle of projection with the vertical is<br/>
Question 111 :
$\text{A diametrical tunnel is dug across the earth. A ball is dropped into the tunnel from one side.}$<br>$\text{ The velocity of the ball when it reaches the centre of the earth is}$<br>$[\text{Given: gravitational potential at the centre of earth} = -\dfrac{ 3 }{2} \left( \dfrac{ GM }{ R } \right)$
Question 112 :
Four particles of masses $m, 2\ m, 3\ m$ and $4\ m$ are kept in sequence at the corners of a square of side $a.$ The magnitude of gravitational force acting on aparticle of mass $m$ placed at the center of the squarewill be.
Question 114 :
Mass particles of 1 kg each are placed along x-axis at x = 1, 2, 4, 8,.....$\infty $ then gravitational field intensity at origin is (G = universal gravitational constant):
Question 115 :
Find the velocity $v$ of the rocket at the moment when its mass is equal to $m$, if at the initial moment it possessed the mass $m_0$ and its velocity was equal to zero.
Question 116 :
If the gravitational force had varied as $r^{-5/2}$ instead of $r^{-2}$; the potential energy of a particle at a distance '$r$' from the centre of the earth would be proportional to
Question 117 :
A particle of mass 'm'describe circular path of radius 'r ' such that its kinetic energy is given by $ K = as^2 $ 's ' is the distance travelled 'a'is constant :
Question 118 :
A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $mv^2/r$ and is directed towards the centre. What is the work done by the force in moving the body half the circumference of the circle.
Question 119 :
If the values of force and length are increased four times then the unit of energy will increases by?
Question 120 :
If $\mathrm{R}=6400\times 10^{3}$ m, g $=9.8\mathrm{m}/\mathrm{s}^{2}$, and if the earth were then reassembled rapidly so that no energy is radiated away, the rise in temperature will be (Given that the specific heat s-1 cal/gm/k)<br/>
Question 121 :
A body of mass $m$ is taken from earth's surface to the height equal to the radius of earth, the change in potential energy will be of
Question 122 :
A body attains a height equal to the radius of theearth when projected from earth' surface. Thevelocity of the body with which it was projected is.
Question 123 :
Two bodies with masses $M_1$ and $M_2$ are initially at the rest and a distance $R$ apart. Then they move directly towards one another under the influence of their mutual gravitational attraction. What is the ratio of the distances traveled by $M_1$ to the distance traveled by $M_2$?
Question 124 :
The gravitational field due to a mass distribution is E=$\dfrac {K} {x^3}$ the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at the a distance x is:
Question 125 :
Displacement of a body is $\displaystyle \left( 5\overline { i } +3\overline { j } -4\overline { k }  \right) m$ when a force $\displaystyle \left( 6\overline { i } +6\overline { j } +4\overline { k }  \right) N$ acts for $5 \ s$. The power in watt is:
Question 126 :
A point $P( \sqrt{3}R,0,0)$ lies on the axis of a ring of a mass $M$ and radius $R$. The ring is located in y-z plane with its centre at origin $O$. A small particle of mass $m$ starts from $P$ and reaches $O$ under gravitational attraction only. Its speed at $O$ will be :<br/>
Question 127 :
If the gravitational acceleration at surface of earth is $ g$, then increase in potential energy in lifting an object of mass $m$ to a height equal to the radius $R$ of earth will be.
Question 128 :
The gravitational potential of two homogenous spherical shells $A$ and $B$ of same surface density at their respective centres are in the ratio $3:4$. If the two shells coalesce into a single one such that surface charge density remains the same, then the ratio of potential at an internal point of the new shell to shell $A$ is equal to<br>
Question 129 :
A particle is moving along with X-axis such that its acceleration is proportional to the displacement from the equilibrium position and they are in the same direction. The displacement x( t) is given by
Question 130 :
A particle of mass $4m$ which is at rest explodes into three fragments. Two of the fragments each of mass $m$ are found to move with a speed $v$ each in mutually perpendicular directions. The energy released in the process of explosion is:
Question 131 :
A tunnel is dug along the diameter ofthe earth. There is a particle of mass $m$ at the centre of the tunnel. Find the minimum velocity given to the particle so that is just reaches to the surface of the earth. $(R =$ radius of earth)
Question 132 :
A comet is highly elliptical orbit around the Sun. The period of the comet's orbit is 90days. Some statements are given regarding the collision between the comet and the earth. Mark the correct statement. [Mass of the Sun$=2\times {10}^{30}$kg, mean distance between the earth and the Sun$=1.5\times {10}^{11}$m]<br>
Question 133 :
A body starts from rest from a point distant ${r}_{0}$ from the centre of the earth. It reaches the surface of the earth whose radius is $R$. the velocity acquired by the body is<br>
Question 134 :
The gravitational force exerted by the Sun on the Moon is about twice as great as the gravitational force exerted by the earth on the Moon, but still Moon is not escaping from the gravitational influence of the earth. Mark the option wich correctly explains the above system.<br>
Question 135 :
Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of $100kg$ and they are $100m$ apart. They are initially at rest relative to one another. how long will it be before the gravitational attraction brings them $1cm$ closer together?<br>
Question 136 :
A projectile is fired vertically upwards from the surface of the earth with a velocity $k{v}_{e}$ where ${v}_{e}$ is the escape velocity and $k<1$. If $R$ is the radius of the earth, the maximum height to which it will rise measured from the centre of earth will be (neglect air resistance)<br>
Question 137 :
A train of mass $m$ moves with a velocity $v$ on the equator from east to west. If  $\omega$ is the angular speed of earth about its axis and $R$ is the radius of the earth then the normal reaction acting on the train is
Question 138 :
In a certain region of space, the gravitational field is given by $-\dfrac {k} {r}$, where r is the distance and k is a constant. If the gravitational potential at$ r = r_0$ be $V_0$, then what is the expression for the gravitational potential (V).
Question 139 :
A system of binary stars of masses ${m}_{A}$ and ${m}_{B}$ are moving in circular orbits of radii ${r}_{A}$ and ${r}_{B}$ respectively. If ${T}_{A}$ and ${T}_{B}$ are the time periods of masses ${m}_{A}$ and ${m}_{B}$ respectively then<br>
Question 140 :
A body starts from rest from a point distance $R_0$ from the centre of the earth of mass M, radius R.. The velocity acquired by the body when it reaches the surface of the earth will be
Question 141 :
Read the assertion and reason carefully to mark the correct option out of the options given below :<br/>Assertion : At height $h$ from ground and at depth $h$ below ground, where h is approximately equal to $0.62 R$, the value of $g$ acceleration due to gravity is same.<br/><br/>Reason : Value of $g$ decreases both sides, in going up and down.
Question 142 :
A person brings amass of $1kg$ from infinity to a pointA lnitially, the mass was at rest but it moves at aspeed of $3 m/s$ as it reaches A. The work done by the person on the mass is $- 5.5 J$The gravitationalpotential at $A$ is
Question 143 :
If the length of the day is $T$, the height of that TVsatellite above the earth's surface which alwaysappears stationary from earth, will be.
Question 144 :
Assume the earth's orbit around the sun is circular and the distance between their centres is D. Mass of the earth is M and its radius is R. If earth has an angular velocity $\omega _{0}$ with respect to its centre and $\omega $ with respect to the centre of the sun, the total kinetic energy of the earth is :<br/>
Question 145 :
The height from the surface of earth at which the gravitational potential energy of a ball of mass $m$ is half of that at the centre of earth is (where $R$ is the radius of earth)<br>
Question 147 :
A body is projected at an angle of $60 ^{0}$ with the horizontal. If its kinetic energy at maximum height is 10 J, then the height at which potential energy and kinetic energy have equal values (consider P.E. at the point of projection to be zero) is :
Question 148 :
The change in potential energy, when a body of mass $m$ is raised to a height $nR$ from the earth's surface is $(R=$ radius of earth$)$
Question 149 :
Two spherical bodies of masses $m$ and $5\ M$ and radii $R$ and $2R$, respectively, are released in free space with initial separation between their centres equal to $12\ R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is<br>
Question 150 :
A particle of mass 10 gm is placed in a potential field given by $V = (50x^2 + 100) \ J/kg$. The frequency of oscillation in cycles/sec is :
