Question 1 :
A particle moves in a circular path with a decreasing speed. Choose the correct statement.
Question 2 : What should be the coefficient of friction between the tyres and the road, when a car travelling at 60 <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97ff2fcb0ee133a281a3d5"> makes a level turn of radius 40 m?
Question 3 : The area o the parallelogram represented by the vectors. <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fff74e70da2c08cb357c"> and <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fff7cf5ae23387f292f5"> is
Question 4 :
When a body moves with a constant speed along a circle
Question 5 :
A cyclist turns around a curve at 15 miles/hour. If the turns at double the speed, the tendency to overturn is
Question 7 :
A stone tied to one end of rope and rotated in a circular motion. If the string suddenly breaks, then the stone travels
Question 8 :
A body of mass 2 kg attached to a string is whirled in a vertical circle of radius 5 m. The minimum speed of the body at lowest point so that the cord does not slacken even at the highest point is
Question 9 :
A particle revolves around a circular path. The acceleration of the particle is
Question 10 :
A car is moving with high velocity when it has a turn. A force acts on it outwardly because of
Question 11 :
A cylindrical vessel partially filled with water is rotated about its vertical central axis. Its surface will
Question 12 :
When a simple pendulum is rotated in a vertical plane with constant angular velocity, the centripetal force is
Question 13 : The maximum velocity <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e98001dcf5ae23387f29375"> with which a car driver must traverse a flat curve of radius 150 <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fed8cf5ae23387f28f3e"> and coefficient of friction 0.6 to avoid skidding is
Question 15 :
The average acceleration vector for a particle having a uniform circular motion is
Question 16 :
A body moves with constant angular velocity on a circle. The magnitude of angular acceleration
Question 17 : A bullet is fired horizontally with a velocity of <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e9800e8cb0ee133a281a9ae"> . During the first second,
Question 18 :
Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long-jump event
Question 19 :
Which of the following statements is false for a particle moving in a circle with a constant angular speed
Question 20 :
A man projects a coin upwards from the gate of a uniformly moving train. The path of coin for the man will be
Question 21 :
A body of mass 5 kg is whirled in a vertical circle by a string 1 m long. Calculate velocity at the top of the circle for just looping the vertical loop
Question 22 :
A wheel completes 2000 revolutions to cover the 9.5 km distance, then the diameter of the wheel is
Question 23 :
In resultant of which of the following sets of forces can not be zero
Question 24 : A vector <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fee84e70da2c08cb2df8"> points vertically upwards and <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fee9cf5ae23387f28f6f"> points upwards North. The vector product <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e98018a4e70da2c08cb3fdc"> is
Question 25 :
A stone is tied at one end of a 5m long string and whirled in a vertical circle. The minimum speed required to just cross the top most position is
Question 26 : A bend in a level road has a radius of 80 m. Find the maximum speed which a car turning the bend may have without skidding, if <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e9802464e70da2c08cb42da">
Question 27 :
A particle is moving in a horizontal circle with constant speed. It has constant
Question 28 :
A body is thrown with a velocity of {tex} 9.8 \mathrm { ms } ^ { - 1 } {/tex} making an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal. It will hit the ground after a time
Question 30 : An aeroplane flying horizontally with a speed of <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e9801334e70da2c08cb3d53"> releases a bomb at a height of 490 m from the ground. When will the bomb strike the ground?
Question 31 :
Which one of the following statements is not correct in a uniform circular motion
Question 32 :
In case of uniform circular motion which of the following physical quantity do not remain constant
Question 33 : A body of mass <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fed8cf5ae23387f28f3e"> moves in a circular path with uniform angular velocity. The motion of the body has constant
Question 35 :
A body of mass 0.4 kg is whirled in a vertical circle making 2rev/s. If the radius of the circle is 2m, then tension in the string when the body is at the top of the circle is
Question 36 : A particle is moving in a circle of radius <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fedb4e70da2c08cb2db1"> with constant speed <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fefccf5ae23387f28fac"> , if radius is double then its centripetal force to keep the same speed should be
Question 38 :
A stone tied with string is rotated in a vertical circle. The minimum speed with which the string has to be rotated
Question 39 :
In an atom for the electron to revolve around the nucleus, the necessary centripetal force is obtained from the following force exerted by the nucleus on the electron
Question 40 :
In uniform circular motion, the velocity vector and acceleration vector are
Question 41 :
A body executing uniform circular motion has at any instant its velocity vector and acceleration vector
Question 42 :
At the top of the trajectory of a projectile, the direction of its velocity and acceleration are
Question 43 :
The force required to keep a body in uniform circular motion is
Question 44 : If a body is projected with an angle <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e97fec8cf5ae23387f28f0c"> to the horizontal then
Question 45 :
A mass of 100 g is tied to one end of string 2 m long. The body is revolving in a horizontal circle making a maximum of 200 revolutions/min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is approximately
Question 47 :
An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blade is
Question 48 : A body of mass 5 kg is moving in a circle of radius 1 m with an angular velocity of 2 <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e9801394e70da2c08cb3d9d"> . The centripetal force, is
Question 49 :
A body is tied to one end of the string and whirled in a vertical circle, the physical quantity which remains constant is
Question 50 :
The time period of the second’s hand of a watch is
Question 51 :
A boatman is stationed at a point on one bank of a river of width {tex} 1 \mathrm { km } . {/tex} The river is flowing at {tex} 5 \mathrm { km } / \mathrm { h } {/tex} and the boatman can row with a speed of {tex} 10 \mathrm { km } / \mathrm { h } {/tex} in still water, the magnitude of the resultant velocity of the boat is
Question 52 :
If rain falls vertically with a velocity {tex} V _ { r } {/tex} and wind blows With a velocity {tex} V _ { w } {/tex} from east to west, then a person standing on the roadside should hold the umbrella in the direction
Question 53 : A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length {tex} s = t ^ { 3 } + 5 , {/tex} where s is in metres and {tex} t {/tex} is in seconds. The radius of the path is 20{tex} \mathrm { m } {/tex} . The acceleration of 'P' when {tex} t = 2 {/tex} s is nearly<br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5d5e75d2e5db655bbf109c03" />
Question 54 : The path of a projectile in the absence of air drag is shown in the figure by dotted line. If the air resistance is not ignored then which one of the path is shown in the figure is appropriate for the projectile <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e9800bfcf5ae23387f295af">
Question 55 :
A gun is aimed at a target in a line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will
Question 56 :
A ship {tex} A {/tex} is moving westwards with a speed of {tex} 10 \mathrm { km } / \mathrm { h } {/tex} and a ship {tex} B , 100 \mathrm { km } {/tex} South of {tex} A , {/tex} is moving Northwards with a speed of {tex} 10 \mathrm { km } / \mathrm { h } {/tex}. The time after which the distance between them becomes shortest, is
Question 57 :
A particle is projected at angle {tex} 37 ^ { \circ } {/tex} with the incline plane in upward direction with speed {tex} 10 \mathrm { m } / \mathrm { s } {/tex}. The angle of incline plane is given {tex} 53 ^ { \circ } . {/tex} Then the maximum height attained by the particle from the incline plane will be
Question 58 :
A truck travelling due north at {tex} 20 \mathrm { m } / \mathrm { s } {/tex} turns west and travels at the same speed. What is the change in velocity?
Question 59 :
At a given instant of time two particles are having the position vectors {tex} 4 \hat { i } - 4 \hat { j } + 7 \hat { k } {/tex} metres and {tex} 2 \hat { i } + 2 \hat { j } + 5 \hat { k } {/tex} metres, respectively. If the velocity of the first particle be {tex} 0.4 \hat { i } \mathrm { ms } ^ { - 1 } {/tex}, the velocity of second particle in metre per second, if they collide after 10 sec is
Question 60 :
A vector of magnitude {tex} b {/tex} is rotated through angle {tex} \theta . {/tex} What is the change in magnitude of the vector?
Question 61 :
A boy playing on the roof of a 10{tex} \mathrm { m } {/tex} high building throws a ball with a speed of 10{tex} \mathrm { m } / \mathrm { s } {/tex} at an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal. How far from the throwing point will the ball be at the height of 10{tex} \mathrm { m } {/tex} from the ground?<br>{tex} \left[ g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } , \sin 30 ^ { \circ } = \frac { 1 } { 2 } , \cos 30 ^ { \circ } = \frac { \sqrt { 3 } } { 2 } \right] {/tex}<br>
Question 62 :
A boat which has a speed of {tex} 5 \mathrm { km } / \mathrm { hr } {/tex} in still water crosses a river of width {tex} 1 \mathrm { km } {/tex} along the shortest possible path in {tex}15{/tex} minutes. The velocity of the river water in {tex} \mathrm { km } / \mathrm { hr } {/tex} is
Question 63 :
A plane flying horizontally at a height of {tex} 1500 \mathrm { m } {/tex} with a velocity of {tex} 200 \mathrm { ms } ^ { - 1 } {/tex} passes directly overhead on antiaircraft gun. Then the angle with the horizontal at which the gun should be fired from the shell with a muzzle velocity of {tex} 400 \mathrm { ms } ^ { - 1 } {/tex} to hit the plane, is
Question 64 :
A cricket ball is hit with a velocity {tex} 25 \mathrm { ms } ^ { - 1 } , 60 ^ { \circ } {/tex} above the horizontal. How far above the ground, ball passes over a fielder {tex} 50 \mathrm { m } {/tex} from the bat (consider the ball is struck very close to the ground)?[Take {tex} \sqrt { 3 } = 1.7 {/tex} and {tex} g = 10 \mathrm { ms } ^ { - 2 } {/tex}]
Question 65 :
A bucket tied at the end of 11.6 m long string is whirled in a vertical circle with a constant speed. The minimum speed at which water from the bucket does not spill when it is the highest position is
Question 66 :
The position of a projectile launched from the origin at {tex} t = 0 {/tex} is given by {tex} \vec { r } = ( 40 \hat { i } + 50 \hat { j } ) \mathrm { m } {/tex} at {tex} t = 2s {/tex} . If the projectile was launched at an angle {tex} \theta {/tex} from the horizontal, then {tex} \theta {/tex} is (take {tex} \left. g = 10 \mathrm { ms } ^ { - 2 } \right) {/tex}
Question 67 :
The equation of a projectile is {tex} y = \sqrt { 3 } x - \frac { g x ^ { 2 } } { 2 } {/tex} The angle of projection is given by
Question 68 :
Two vectors {tex} \vec { A } {/tex} and {tex} \vec { B } {/tex} are such that {tex} \vec { A } - \vec { B } = \vec { C } {/tex} and {tex} A - B = C . {/tex} The angle between them is
Question 69 :
A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is 0.5 {tex}\mathrm { m } / \mathrm { s } {/tex} at an angle of {tex} 120 ^ { \circ } {/tex} with the direction of flow of water. The speed of water is
Question 70 :
A projectile is fired at an angle of {tex} 45 ^ { \circ } {/tex} with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection is
Question 71 :
If {tex} \mathrm { Vr } {/tex} is the velocity of rain falling vertically and {tex} \mathrm { Vm } {/tex} is the velocity of a man walking on a level road, and {tex} \theta {/tex} is the angle with vertical at which he should hold the umbrella to protect himself, than the relative velocity of rain w.r.t. the man is given by:
Question 72 :
When a body moves in a circular path, no work is done by the force since
Question 73 :
A projectile is fired from the surface of the earth with a velocity of {tex} 5 \mathrm { ms } ^ { - 1 } {/tex} and angle {tex} \theta {/tex} with the horizontal. Another projectile fired from another planet with a velocity of {tex} 3 \mathrm { ms } ^ { - 1 } {/tex} at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is ( in {tex} \left. \mathrm { ms } ^ { - 2 } \right) {/tex} given {tex} \mathrm { g } = 9.8 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex}.
Question 74 :
If a vector {tex} 2 \hat { \mathrm { i } } + 3 \hat { \mathrm { j } } + 8 \hat { \mathrm { k } } {/tex} is perpendicular to the vector {tex} 4 \hat { \mathrm { j } } - 4 \hat { \mathrm { i } } + \alpha \hat { \mathrm { k } } , {/tex} then the value of {tex} \alpha {/tex} is
Question 75 :
Assertion: A glass ball is dropped on concrete floor can easily get broken compared if it is dropped wooden floor.
Reason: On concrete floor glass ball will take less time to come to rest.
Question 76 :
A particle moves in a circle of radius {tex} 30 \mathrm { cm } . {/tex} Its linear speed is given by: {tex} \mathrm { V } = 2 \mathrm { t } , {/tex} where in second and {tex} \mathrm { v } {/tex} in {tex} \mathrm { m } / \mathrm { s } {/tex}. Find out its radial and tangential acceleration at {tex} \mathrm { t } = 3 {/tex} sec respectively.
Question 77 : If {tex} \mathrm V_1 {/tex} is velocity of a body projected from the point {tex} \mathrm A {/tex}and {tex} \mathrm V _2 {/tex} is the velocity projected from point {tex} \mathrm B {/tex} which is vertically below the highest point {tex} \mathrm C {/tex} , if both the bodies collide, then <br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5df31d3e8701466b65e04ddf"><br>
Question 78 : An aircraft moving with a speed of 250{tex} \mathrm { m } / \mathrm { s } {/tex} is at a height of {tex} 6000 \mathrm { m } , {/tex} just overhead of an anti aircraft-gun. If the muzzle velocity is {tex} 500 \mathrm { m } / \mathrm { s } , {/tex} the firing angle {tex} \theta {/tex} should be:<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5d5e75a4e5db655bbf109bd6"><br>
Question 79 :
Which of the following is/are correct?<br> I. {tex} \vec { A } \times \vec { B } = - \vec { B } \times A {/tex} <br>II. {tex} \vec { A } \times \vec { B } \neq \vec { B } \times A {/tex} <br>III. {tex} \vec { A } \times ( \vec { B } + \vec { C } ) = ( \vec { A } \times \vec { B } ) + \vec { C } {/tex}
Question 80 :
Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity {tex} v {/tex} and other with a uniform acceleration {tex} a {/tex} . If {tex} \alpha {/tex} is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by
Question 81 :
A particle is moving eastwards with a velocity of {tex} 5 \mathrm { m } / \mathrm { s } {/tex}. In {tex}10 {/tex}seconds the velocity changes to {tex} 5 \mathrm { m } / \mathrm { s } {/tex} northwards. The average acceleration in this time is
Question 82 :
Two racing cars of masses {tex} \mathrm { m } _ { 1 } {/tex} and {tex} \mathrm { m } _ { 2 } {/tex} are moving in circles of radii {tex} \mathrm { r } _ { 1 } {/tex} and {tex} \mathrm { r } _ { 2 } {/tex} respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is
Question 83 :
A body {tex} A {/tex} begins to move with initial velocity {tex}2 \mathrm { m } / \mathrm { sec } {/tex} and continues to move at a constant acceleration {tex} a \cdot \Delta t = 10 \mathrm { seconds } {/tex} after the body {tex} A {/tex} begins to move a body {tex} B {/tex} departs from the same point with an initial velocity {tex} 12 \mathrm { m } / \mathrm { sec } {/tex} and moves with the same acceleration {tex} a {/tex}. What is the maximum acceleration {tex} a {/tex} at which the body {tex} B {/tex} can overtake {tex} A ? {/tex}
Question 84 : An aircraft moving with a speed of {tex} 250 \mathrm { m } / \mathrm { s } {/tex} is at a height of {tex} 6000 \mathrm { m } , {/tex} just overhead of an anti aircraft gun. If the muzzle velocity is {tex} 500 \mathrm { m } / \mathrm { s } {/tex}, the firing angle {tex} q {/tex} should be:<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc59de50f934b847a59af">
Question 85 :
Two forces have magnitudes in the ratio {tex}3: 5{/tex} and the angle between their directions is {tex} 60 ^ { \circ } . {/tex} If their resultant is {tex} 35 \mathrm { N } , {/tex} their magnitudes are
Question 86 :
Two balls are rolling on a flat surface. One has velocity components {tex} 1 \mathrm { m } / \mathrm { s } {/tex} and {tex} \sqrt { 3 } \mathrm { m } / \mathrm { s } {/tex} along the rectangular axes {tex} x {/tex} and {tex} y , {/tex} respectively, and the other has components {tex} 2 \mathrm { m } / \mathrm { s } {/tex} and {tex} 2 \mathrm { m } / \mathrm { s } {/tex}, respectively. If both the balls start moving from the same point, the angle between their directions of motion is
Question 87 :
The vector having magnitude equal to 3 and perpendicular to the two vectors {tex} \overrightarrow { \mathbf { A } } = 2 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } } + \hat { \mathbf { k } } {/tex} and {tex} \overrightarrow { \mathbf { B } } = 2 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } } + 3 \hat { \mathbf { k } } {/tex} is:
Question 88 :
If {tex} \overrightarrow { \mathrm { A } } = 4 \hat { \mathrm { i } } + 3 \hat { \mathrm { j } } {/tex} and {tex} \overrightarrow { \mathrm { B } } = 3 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } {/tex} then cosine of angle between {tex} \overrightarrow { \mathrm { A } } {/tex} and {tex} \overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } } {/tex} is
Question 89 :
A particle moves in a circle of radius {tex} 30 \mathrm { cm } . {/tex} Its linear speed is given by : {tex} \mathrm { v } = 2 \mathrm { t } , {/tex} where {tex} \mathrm { t } {/tex} in second and {tex} \mathrm { v } {/tex} in {tex} \mathrm { m } / \mathrm { s } {/tex}. Find out its radial and tangential acceleration at {tex} \mathrm { t } = 3 \mathrm { sec } {/tex} respectively.
Question 90 : For an observer on trolley direction of projection of particle is shown in the figure, while for observer on ground ball rise vertically. The maximum height reached by ball from trolley is <br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5e0ddbcc33674517c21e09e2.jpg" />
Question 91 : The velocity {tex} \overrightarrow { \mathrm { v } } {/tex} of a particle moving in the {tex} x y - {/tex} plane is given by {tex} \overrightarrow { \mathrm { v } } = \left( 6 t - 4 t ^ { 2 } \right) \hat { \mathrm { i } } + 8 \hat { \mathrm { j } } , {/tex} with {tex} \overrightarrow { \mathrm { v } } {/tex} in {tex} \mathrm { m } / \mathrm { s } {/tex} and {tex} \mathrm { t } ( > 0 ) {/tex} in second.<br>Match the following Columns:<br><table>
<tr><th>Column I</th> <th>Column II</th> </tr>
<tr><td>(A)Aceleration magnitude is {tex}10\mathrm {m/s}^2{/tex} at a time</td> <td>(1){tex}3/4\mathrm s{/tex}</td> </tr>
<tr><td>(B)Acceleration zero at time</td> <td>(2) never</td> </tr>
<tr><td>(C)velocity zero at time </td> <td>(3){tex}1\mathrm s{/tex}</td> </tr>
<tr><td>(D)The speed {tex}10\mathrm {m/s} {/tex} at a time</td> <td>(4){tex}2\mathrm s{/tex}</td> </tr>
</table>
Question 92 :
Two balls are projected at an angle {tex} \theta {/tex} and {tex} \left( 90 ^ { \circ } - \theta \right) {/tex} to the horizontal with the same speed. The ratio of their maximum vertical heights is
Question 93 :
A river is flowing from west to east at a speed of {tex}5{/tex} metres per minute. A man on the south bank of the river, capable of swimming at {tex}10{/tex} metres per minute in still water, wants to swim across the river to a point directly opposite in shortest time. He should swim in a direction
Question 94 :
If {tex}\mathrm u{/tex} is the initial velocity of a projectile and {tex}\mathrm v{/tex} is the velocity at any instant, then the maximum horizontal range {tex} \mathrm { R } _ { \mathrm { m } } {/tex} is equal to
Question 95 :
A particle is moving such that its position coordinate (x, y) are<br> (2m, 3m) at time t = O <br> (6m, 7m) at time t = 2s and<br> (13m, 14m) at time t=5s<br> Average velocity vector ({tex} \vec {V_{av}}{/tex})from t = 0 to t = 5s is:
Question 96 :
A boat which has a speed of {tex} 5 \ \mathrm { km } / \mathrm { hr } {/tex} in still water crosses a river of width {tex} 1 \ \mathrm { km } {/tex} along the shortest possible path in {tex} 15 \ \mathrm { minutes. } {/tex} The velocity of the river water in {tex} \mathrm { km } / \mathrm { hr } {/tex} is
Question 97 :
A particle dropped from the top of a tower uniformly falls on ground at a distance which is equal to the height of tower. Which of the following paths will be transversed by the particle?
Question 98 :
If {tex} \vec { a } , \vec { b } {/tex} and {tex} \vec { c } {/tex} are three unit vectors such that {tex} \vec { a } + \vec { b } + \vec { c } = 0 {/tex} then the value of {tex} \vec { a } \cdot \vec { b } + \vec { b } \cdot \vec { c } + \vec { c } . \vec { a } {/tex} is
Question 99 :
Two particles {tex} A {/tex} and {tex} B {/tex} separated by a distance {tex} 2 R {/tex} are moving counter clockwise along the same circular path of radius {tex} R {/tex} each with uniform speed {tex} v . {/tex} At time {tex} t = 0 , {/tex} {tex} A {/tex} is given a tangential acceleration of magnitude {tex} a = \frac { 72 v ^ { 2 } } { 25 \pi R } {/tex} then {tex} \quad {/tex}
Question 100 :
One of the two forces is double the other and their resultant is equal to the greater force. The angle between them is
Question 101 :
Two boys are standing at the ends {tex} A {/tex} and {tex} B {/tex} of a ground where {tex} A B = a {/tex} . The boy at {tex} B {/tex} starts running in a direction perpendicular to {tex} A B {/tex} with velocity {tex} v _ { 1 } {/tex} . The boy at {tex} A {/tex} starts running simultaneously with velocity {tex} v {/tex} and catches the other boy in a time {tex} t , {/tex} where {tex} t {/tex} is
Question 102 :
The position vectors of points {tex} \mathrm { A } , \mathrm { B } , \mathrm { C } {/tex} and {tex} \mathrm { D } {/tex} are {tex} \mathrm { A } = 3 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } + 5 \hat { \mathrm { k } } , \mathrm { B } = 4 \hat { \mathrm { i } } + 5 \hat { \mathrm { j } } + 6 \hat { \mathrm { k } } , \mathrm { C } = 7 \hat { \mathrm { i } } + 9 \hat { \mathrm { j } } + 3 \hat { \mathrm { k } } {/tex} and {tex} \mathrm { D } = 4 \hat { \mathrm { i } } + 6 \hat { \mathrm { j } } {/tex} then the displacement vectors {tex} \overline { \mathrm { AB } } {/tex} and {tex} \overline { \mathrm { CD } } {/tex} are
Question 103 :
A car runs at a constant speed on a circular track of radius {tex} 100 \mathrm { m } , {/tex} taking 62.8 seconds in every circular loop. The average velocity and average speed for each circular loop respectively, is
Question 104 :
For a particle in uniform circular motion, the acceleration {tex} \vec { a } {/tex} at a point {tex} \mathrm { P } ( \mathrm { R } , \theta ) {/tex} on the circle of radius {tex} \mathrm { R } {/tex} is (Here {tex} \theta {/tex} is measured from the {tex} \mathrm { x } {/tex} -axis)
Question 105 :
A man running along a straight road with uniform velocity {tex} \overrightarrow { \mathrm { u } } = u \hat { \mathrm { i } } {/tex} feels that the rain is falling vertically down along {tex} - \hat { \mathrm { j } } {/tex} . If he doubles his speed, he finds that the rain is coming at an angle {tex} \theta {/tex} with the vertical. The velocity of the rain with respect to the ground is
Question 106 :
A particle is projected with a velocity {tex} v {/tex} such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where {tex} g {/tex} is acceleration due to gravity)
Question 107 :
A bullet is fired with a speed of {tex} 1500 \mathrm { m } / \mathrm { s } {/tex} in order to hit a target {tex} 100 \mathrm { m } {/tex} away. If {tex} \mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} The gun should be aimed
Question 108 :
Two pegs {tex} A {/tex} and {tex} B {/tex} thrown with speeds in the ratio {tex}1: 3{/tex} acquired the same heights. If {tex} A {/tex} is thrown at an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal, the angle of projection of {tex} B {/tex} will be
Question 109 :
The velocity of projection of oblique projectile is {tex} ( 6 \hat { \mathrm { i } } + 8 \hat { \mathrm { j } } ) \mathrm { ms } ^ { - 1 } {/tex} . The horizontal range of the projectile is
Question 110 :
Two particles {tex} A {/tex} and {tex} B {/tex} separated by a distance {tex} 2 R {/tex} are moving counter clockwise along the same circular path of radius {tex} R {/tex} each with uniform speed {tex} v {/tex}. At time {tex} t = 0 , A {/tex} is given a tangential acceleration of magnitude {tex} a = \frac { 72 v ^ { 2 } } { 25 \pi R } {/tex} then
Question 111 :
A stone tied to the end of a string of {tex} 1 \mathrm { m } {/tex} long is whirled in a horizontal circle with a constant speed. If the stone makes {tex}22 {/tex} revolution in {tex}44{/tex} seconds, what is the magnitude and direction of acceleration of the stone?
Question 112 :
Two boats {tex} A {/tex} and {tex} B , {/tex} move away from a buoy anchored at the middle of a river along the mutually perpendicular straight lines: the boat {tex} A {/tex} along the river and the boat {tex} B {/tex} across the river. Having moved off an equal distance from the buoy the boats returned. What is the ratio of times of motion of boats {tex} \frac { \tau _ { A } } { \tau _ { B } } , {/tex} if the velocity of each boat with respect to water is 1.2 times greater than the stream velocity.
Question 113 : A particle is projected with some angle from the surface of the planet. The motion of the particle is described by the equation; {tex} x = t , y = t - t ^ { 2 } {/tex}. Then match the following columns:<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5df31d368701466b65e04dd8"><br>
Question 114 :
Two pegs {tex} A {/tex} and {tex} B {/tex} thrown with speeds in the ratio {tex} 1: 3 {/tex} acquired the same heights. If {tex} A {/tex} is thrown at an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal, the angle of projection of {tex} B {/tex} will be
Question 115 :
A ball rolls off to the top of a staircase with a horizontal velocity {tex} \mathrm { u } \ \mathrm { m } / \mathrm { s } {/tex}. If the steps are {tex}h{/tex} metre high and {tex}b{/tex} metre wide, the ball will hit the edge of the {tex} \mathrm n^{th}{/tex} step, if
Question 116 :
Rain, pouring down at an angle {tex} \alpha {/tex} with the vertical has a speed of {tex} 10 \mathrm { ms } ^ { - 1 } {/tex}. A girl runs against the rain with a speed of {tex} 8 \mathrm { ms } ^ { - 1 } {/tex} and sees that the rain makes an angle {tex} \beta {/tex} with the vertical, then relation between {tex} \alpha {/tex} and {tex} \beta {/tex} is
Question 117 :
A projectile is thrown in the upward direction making an angle of {tex} 60 ^ { \circ } {/tex} with the horizontal direction with a velocity of {tex} 147 \mathrm { ms } ^ { - 1 } {/tex}. Then the time after which its inclination with the horizontal is {tex} 45 ^ { \circ } , {/tex} is
Question 118 :
{tex}\mathbf {Assertion} {/tex} : The horizontal range is same when the angle of projection is greater than {tex} 45 ^ { \circ } {/tex} by certain value and less than {tex} 45 ^ { \circ } {/tex} by the same value.<br>{tex}\mathbf {Reason} {/tex} : If {tex} \theta = 45 ^ { \circ } + \alpha {/tex}, then {tex} R _ { 1 } = \frac { u ^ { 2 } \sin 2 \left( 45 ^ { \circ } + \alpha \right) } { g } = \frac { u ^ { 2 } \cos 2 \alpha } { g }{/tex} .<br>If {tex} \theta = 45 ^ { \circ } - \alpha , {/tex} then {tex} R _ { 2 } = \frac { u ^ { 2 } \sin 2 \left( 45 ^ { \circ } - \alpha \right) } { g } = \frac { u ^ { 2 } \cos 2 \alpha } { g } {/tex}<br>
Question 119 : A ball is thrown at an angle {tex} 75 ^ { \circ } {/tex} with the horizontal at a speed of {tex} 20 \mathrm { m } / \mathrm { s } {/tex} towards a high wall at a distance d. If the ball strikes the wall, its horizontal velocity component reverses the direction without change in magnitude and the vertical velocity component remains same. Ball stops after hitting the ground. Match the statement of {tex}\mathrm{ Column\ I}{/tex} with the distance of the wall from the point of throw in {tex}\mathrm{ Column\ II}{/tex}<br><br><table>
<tr><th>Column I </th> <th>Column II</th> </tr>
<tr><td>(A)Ball strikes the wall directly </td> <td>(1)8m</td> </tr>
<tr><td>(B)Ball strikes the ground at x=12m from the wall</td> <td>(2)10m</td> </tr>
<tr><td>(C)Ball strikes the ground at x=10m from the wall</td> <td>(3)0m</td> </tr>
<tr><td>(D)Ball strikes the ground at x=5m from the wall</td> <td>(4)25m</td> </tr>
</table>
Question 120 :
Three points are located at the vertices of an equilateral triangle whose side equal to {tex} a {/tex}. They all start moving simultaneously with velocity {tex} v {/tex} constant in modulus, with first point heading continually for the second, the second for the third, and the third for the first. How soon will the points converge?
Question 121 :
A projectile is thrown in the upward direction making an angle of {tex} 60 ^ { \circ } {/tex} with the horizontal direction with a velocity of {tex} 147 \mathrm { ms } ^ { - 1 } {/tex}. Then the time after which its inclination with the horizontal is {tex} 45 ^ { \circ } , {/tex} is
Question 122 :
A cricket ball thrown across a field is at heights {tex} h _ { 1 } {/tex} and {tex} h _ { 2 } {/tex} from point of projection at times {tex} t _ { 1 } {/tex} and {tex} t _ { 2 } {/tex} respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is
Question 123 :
The greatest range of a particle, projected with a given velocity on an inclined plane, is {tex} x {/tex} times the greatest vertical altitude above the inclined plane. Find the value of {tex} x . {/tex}
Question 124 : Two particles are projected simultaneously from the level ground as shown in figure. They may collide after a time:<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc5e5e50f934b847a59ed">
Question 125 :
A particle is projected with a certain velocity at an angle {tex} \alpha {/tex} above the horizontal from the foot of an inclined plane of inclination {tex} 30 ^ { \circ } . {/tex} If the particle strikes the plane normally then {tex} \alpha {/tex} is
Question 126 : Two identical particles are projected horizontally in opposite directions with a speed of {tex} 5 \mathrm { ms } ^ { - 1 } {/tex} each from the top of a tall tower as shown. Assuming {tex} \mathrm { g } = 10 \mathrm { ms } ^ { - 2 } {/tex}, the distance between them at the moment when their velocity vectors become mutually perpendicular is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc675e50f934b847a5a64"><br>
Question 127 :
If a particle is projected with speed {tex} u {/tex} from ground at an angle with horizontal, then radius of curvature of a point where velocity vector is perpendicular to initial velocity vector is given by
Question 128 :
The velocity of projection of a body is increased by {tex} 2 \% {/tex}. Other factors remaining unchanged, what will be the percentage change in the maximum height attained?
Question 129 :
A particle describes uniform circular motion in a circle of radius {tex} 2 \ \mathrm { m } , {/tex} with the angular speed of {tex} 2 \ \mathrm { rad } \mathrm { s } ^ { - 1 } . {/tex} The magnitude of the change in its velocity in {tex} \frac { \pi } { 2 } \mathrm { s } {/tex} is
Question 130 :
If retardation produced by air resistance of projectile is one-tenth of acceleration due to gravity, the time to reach maximum height
Question 131 : A projectile of mass {tex} \mathrm { m } {/tex} is thrown with a velocity v making an angle {tex} 60 ^ { \circ } {/tex} with the horizontal. Neglecting air resistance, the change in velocity from the departure A to its arrival at B, along the vertical direction is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc58de50f934b847a59a3">
Question 132 :
For angle {tex} \ldots \mathrm { X } \ldots , {/tex} the projectile has maximum range and it is equal to {tex} \ldots \mathrm { Y } \ldots {/tex} Here, {tex} \mathrm { X } {/tex} and {tex} \mathrm { Y } {/tex} refer to
Question 133 :
A particle moves along a circle of radius {tex} \left( \frac { 20 } { \pi } \right) \mathrm { m } {/tex} with constant tangential acceleration. It the velocity of particle is <b>80m/s</b> at end of second revolution after motion has begun, the tangential acceleration is
Question 134 : A particle<b>P</b> is projected from a point on the surface of smooth inclined plane ( see figure). Simultaneously another particle <b>Q</b> is released on the smooth inclined plane from the same position. <b>P</b> and <b>Q</b> collide on the inclined plane after <b>t = 4 s</b>. The speed of projection of <b> P </b> is:<center> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/NEET/5ece589b0e3719389a31f981' class="uploaded-image" /> </center>
Question 135 :
{tex} \mathbf {Assertion} {/tex} : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths.<br>{tex} \mathbf {Reason} {/tex} : For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same.<br>
Question 136 :
A stone is just released from the window of a moving train moving along a horizontal straight track. The stone will hit the ground following a
Question 137 :
If {tex} \overrightarrow { \mathrm { A } } = \hat { \mathrm { i } } + \hat { \mathrm { j } } + \hat { \mathrm { k } } {/tex} and {tex} \overrightarrow { \mathrm { B } } = 2 \hat { \mathrm { i } } - \hat { \mathrm { j } } + 4 \hat { \mathrm { k } } {/tex} then the unit vector along {tex} \overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } } {/tex} is
Question 138 :
For motion in two or three dimensions, the angle between velocity and acceleration is
Question 139 :
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is
Question 140 :
A projectile is thrown in the upward direction making an angle of {tex} 60 ^ { \circ } {/tex} with the horizontal direction with a velocity of {tex} 147 \ \mathrm { ms } ^ { - 1 } . {/tex} Then the time after which its inclination with the horizontal is {tex} 45 ^ { \circ } , {/tex} is
Question 141 :
A particle crossing the origin of co-ordinates at time {tex} \mathrm { t } = 0 , {/tex} moves in the xy-plane with a constant acceleration {tex}a{/tex} in the y-direction. If its equation of motion is {tex} \mathrm { y } = \mathrm { bx } ^ { 2 } {/tex} (b is a constant), its velocity component in the x-direction is
Question 142 :
It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation {tex} 5 \pi / 36 {/tex} rad should strike a given target. In actual practice, it was found that a hill just prevented the trajectory. At what angle (rad) of elevation should the gun be fired to hit the target
Question 143 :
If the angles of projection of a projectile with same initial velocity exceed or fall short of {tex} 45 ^ { \circ } {/tex} by equal amounts, then the ratio of horizontal ranges is
Question 144 :
A particle moves in the {tex} \mathrm { X } - \mathrm { Y } {/tex} plane with a constant acceleration {tex} 1.5 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} in the direction making an angle of {tex} 37 ^ { \circ } {/tex} with the {tex} \mathrm { X } {/tex} -axis. At {tex} \mathrm t = 0 {/tex} the particle is at the origin and its velocity is {tex} 8.0 \mathrm { m } / \mathrm { s } {/tex} along the {tex} \mathrm { X } {/tex}-axis. Find the position of the particle at {tex} \mathrm t = 4.0 \mathrm { s } {/tex}.
Question 145 :
A body is projected vertically upwards with a velocity {tex} u , {/tex} after time {tex} t {/tex} another body is projected vertically upwards from the same point with a velocity {tex} v , {/tex} where {tex} v < u {/tex}. If they meet as soon as possible, then choose the correct option
Question 146 :
A particle of unit mass is projected with velocity {tex} u {/tex} at an inclination {tex} \alpha {/tex} above the horizon in a medium whose resistance is {tex} k {/tex} times the velocity. Its direction will again make an angle {tex} \alpha {/tex} with the horizon after a time
Question 147 : A {tex} 2 \mathrm { m } {/tex} wide truck is moving with a uniform speed {tex} v _ { 0 } = 8 \mathrm { m } / \mathrm { s } {/tex} along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed {tex} v {/tex} when the truck is {tex}4 \mathrm { m } {/tex} away from him. The minimum value of {tex} v {/tex} so that he can cross the road safely is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc657e50f934b847a5a4c">
Question 148 :
A body is projected vertically upwards with a velocity {tex} u , {/tex} after time {tex} t {/tex} another body is projected vertically upwards from the same point with a velocity {tex} v , {/tex} where {tex} v < u {/tex}. If they meet as soon as possible, then choose the correct option
Question 149 :
A balloon starts rising from the surface of the earth. The ascension rate is constant and equal to {tex} v _ { 0 } {/tex}. Due to the wind the balloon gathered the horizontal velocity component {tex} v _ { x } = a y , {/tex} where {tex}a{/tex} is a constant and {tex} y {/tex} is the height of ascent. The tangential, acceleration of the balloon is
Question 150 :
A small cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?
