# Q.1 A particle is moving in a straight line with initial velocity u and retardation α v, where v is the velocity at any time t [a] the particle will cover a total distance u/ α [b] the particle will come to rest after 1/ α [c] the particle will continue to move for a very long time [d] the velocity of the particle will become u/2 after time 1/ α Q.2 A particle moves along the xaxis as x = u(t-1) 2 + a(t-3) 3 [a] initial velocity of the particle is u [b] the acceleration of the particle is a [c] the acceleration of the particle is 2a [d] the particle is at the origin at time t=3 seconds Q.3 A particle is projected vertically upwards [a] the speed decreases uniformly with distance [b] the speed decreases uniformly with time [c] the KE decrease uniformly with time [d] KE decreases uniformly with distance Q.4 If an observer moves at constant speed along the line joining two stationary objects> he will the two objects [a] have the same velocity [b] have the same speed [c] move in opposite directions [d] move in the same direction. Q.5 A particle is moving with uniform acceleration along a straight line AB. Its speed at A and B are 2m/s and 14m/s respectively. Then [a] its speed at the midpoint is 10m/s [b] its speed at point P such that AP:PB is 1:5 is 4m/s [c] the time to go from A to mid point of AB is double to move from mid point to B [d] none of the above. Q.6 A body starting from rest is moving with uniform acceleration of 5m/s 2 for time 10s, and after that with uniform acceleration of 10m/s 2 for 15s, then [a] average acceleration of the body is 7.5m/s 2 [b] the average acceleration is 8m/s 2 [c] total distance covered is 1875m [d] total distance covered is 2125m Q.7 A particle moves first 10m in 2s and 20m in the next 3s and 30m in next 10s. which of the following statements are true for motion? [a] the particle is moving with uniform velocity [b] the average speed of the particle is 4m/s [c] the particle is uniformly accelerated [d] the particle has deceleration during the motion Q.8 Suppose a and v denoted the acceleration and velocity vector if the body in one dimensional motion: [a] speed must increase if a > 0 [b] speed must increase if v and a >0 [c] speed must decrease if a [d] speed will decrease if v 0 Q.9 The motion of the particle falling in the restive medium is given by dv/dt = A-Bv where A and B are constants. Then [a] the initial acceleration of the body is A [b] the velocity at which the acceleration becomes zero is A/B [c] the velocity at any time t is A(1-e -Bt )/B [d] all the above are wrong Q.10 The displacement of the particle depends upon time as x = α t 2 – β t 3 [a] the particle will come to rest after time t=2 α /3 β [b] the particle will return to the starting point after time α / β [c] no net force acts on the particle at t= α /3 β [d] the initial velocity of the particle was zero but initial acceleration was not zero. Q.11 A lead ball is dropped into a lake from a diving board 5m above the water. If it hits the water with certain velocity and sinks to the bottom with same constant velocity. It reaches the bottom 5s after it is dropped. [a] the depth of the lake is 40m [b] the depth of the lake is 50m [c] the average velocity of the ball is 5m/s [d] the average velocity of the ball is 9m/s Q.12 A balloon starts rising from the ground with an acceleration of 2.5m/s 2 . after 4 seconds the stone is relased from the balloon. If g=10m/s 2 . The stone will [a] have displacement of 25m [b] cover a total distance of 30m [c] reach the ground in 3.2s [d] begins to move down after it is released. Q.13 Which of the following about distance are true? [a] it can’t be negative [b] it can be zero [c] it can be lesser than the magnitude of the displacement [d] it can never decrease with time Q.14 A particle of mass m moves on the x axis as follows. It starts from rest t t=0 from the point x=0 and comes to rest at time t=1 at the point x=1. No other information is available about intermediate times. If α denotes acceleration, then [a] α cannot remain positive for all values of time between 0 and 1 [b] cannot exceed 2 at any pont in its path [c] must be 4 at some point on its path [d] α must change sign during motion but no other assertion can be made Q.15 A ball is dropped from the window of a train moving with uniform velocity. The ball will reach the ground following a [a] parabolic path for the passenger [b] parabolic path for man standing on the ground [c] straight line path for the passenger [d] none of these Q.16 A particle starts moving along a straight line with velocity of 10m/s. after 5 seconds the distance of the particle from the starting point is 50m. which of the following statement is true about the motion of the particle is true? [a] the motion may be with constant acceleration [b] the motion may be with the constant velocity [c] the motion may be continuously retarded [d] motion may be first accelerated and then retarded Q.17 A body is dropped from the top of the tower of height h. it covers a distance h/3 in last minute of its motion. If g=10m/s 2 , how much time does it take to reach the ground? [a] 2 + √ 3s [b]2- √ 3 s [c] 3+ √ 6s [d] 3- √ 6 s Q.18 A Car starting from rets has a constant acceleration a 1 for time interval t 1 during which it covers a distance s 1 . In the next time interval t 2 the car has retardation a 2 and comes to rest after covering distance s 2 in time t 2 . the average speed of the car during the journey is given by [a] a 1 t 1 /2 [b]a 2 t 2 /2 [c][a 1 +a 2 ][t 1 +t 2 ’4 [d]zero Q.19 a man throws a stone vertically upwards with a speed of 20m/s from the top of the high rise building. Two seconds later, an identical stone is thrown vertically downwards with speed of 20m/s. then: [a] the relative velocity between the two stones remains constant till one hits the ground [b] both will have the same kinetic energy when they hit the ground [c] the time interval between their hitting the ground is 2s [d] if the collision with the ground is perfectly elastic both will rise to the same height above the ground Q.20 An aeroplane flis along the straight line from A to B with speed V and back again with the same speed. If there is steady wind speed v. the distance between A and B is l [a] total time for the round trip, if wind blows along the line AB is 2V/[V 2 -v 2 ] [b] total time for round trip if the wind blows perpendicular to AB is 2V/[V 2 -v 2 ] [c] total time for round trip is always increased by the presence of the wind [d] total time for round trip depends on the direction of the trip Q.21 A particle starts from origin with coordinates at time t=0 and moves in th e x-y plane with constant acceleration α in the y direction. Its equation of motion is y= β x 2 . its velocity component in the x direction is equal to [a]variable [b] α/2β [c] [d] Projectile Motion Q.1 A body is projected at an angle of 30 0 to the horizontal with a speed of 30m/s. what is angle with the horizontal after 1.5 seconds? [a] 0 0 [b] 30 0 [c] 60 0 [d] 90 0 Q.2 A projectile is thrown with the initial velocity of 50m/s. the maximum horizontal distance this projectile can travel is [a] 64m [b] 128m [c] 5m [d] 255m Q.3 The range of projectile which is launched at an angle of 15 0 with the horizontal is 1.5km. what is the range of projectile which is fired at an angle of 45 0 with same speed? [a] 1.5km [b] 3km [c] 6km [d] 0.75km Q.4 When air resistance is taken into account while dealing with the motion of the projectile which of the following properties shows an increase? [a] range [b] maximum height [c] speed with which it strikes the ground [d] the angle at which the projectile hits the ground Q.5 A ball rolls off the edge of the stairway with a horizontal velocity of magnitude 1.8m/s. the steps are 0.2m high and 0.2m wide. Which step will ball hit first? [a] first [b] second [c] third [d] fourth Q.6 A hunter aims at the monkey sitting on a tree at considerable distance. At the instant he fires at it the monkey drops. Will the bullet hit the monkey? [a] no [b] yes [c] sometimes [d] never Q.7 The angle of projection, which for which the horizontal range and maximum height are equal is [a] 45 0 [b] tan -1 [4] [c] tan -1 [0.25] [d] none of these Q.8 The height y and the distance along horizontal traveled by projectile is given by y = 8t-5t 2 and x=6t. the velocity of projection is [a] 8m/s [b] 6m/s [c] 10m/s [d] can’t be found Q.9 A body is projected at an angle of 30 0 to the horizontal with kinetic energy E. the KE at the highest point is [a] zero [b] E/4 [c] E/2 [d] 3E/4 Q.10 In projectile motion the angle between the velocity and acceleration at the highest point is [a] 45 0 [b] 30 0 [c] 90 0 [d] 0 0 Q.11 A man can throw a stone to maximum horizontal distance of 80m. the maximum height to which he can throw is [a] 10m [b] 20m [c] 30m [d] 40m Q.12 A gun fired two bullets at 60 0 and 30 0 with horizontal. The bullets strike at same horizontal distance. The ratio of maximum heights in the two cases is [a] 1:1 [b] 2;1 [c] 3:1 [d] 4:1 Q.13 Which of the following does not affect the maximum height attained by the projectile? [a] acceleration of the projectile [b] magnitude of the initial velocity [c] mass of the projectile [d] angle of projection Q.14 In projectile motion, the velocity [a] is never perpendicular to the acceleration [b] is always perpendicular to the acceleration [c] is perpendicular to acceleration at one instant only [d] is perpendicular to acceleration at two instants only. Q.15 A ball rolls off the top of the stairway with velocity um/s in horizontal direction. If the steps are h meters high and b meter wide, the ball will hit the edge of nth step where n is [a] 2hu/gb 2 [b] 2hu 2 /gb 2 [c] 2hu 2 /gb [c] hu 2 /gb 2 Q.16 An arrow is projected into air. Its times of flight is 5 second and range 200m. what is maximum height reached by it? [a] 31.25m [b] 24.5m [c] 18.25m [d] 46.75m Q.17 A ball is thrown from the ground with a velocity of 20 √ 3 m/s making an angle of 60 0 with the horizontal. The ball will be at the height of 40m from the ground after a time of [a] √ 2 second [b] √ 3m/s [c] 2 second [d] 3 seconds. Q.18 A projectile of mass 100gm is fired with a velocity of 20m/s making an angle of 30 0 with the horizontal. As it rises to the highest point of its path, its momentum changes by [a] 1/2kgm/s [b] 1kgm/s [c] 2kgm/s [d] none of these Q.19 From certain height, two bodies are projected horizontally with velocities 10m/s and 20m/s. they will hit the ground in time t 1 and t 2 second., then [a] t 1 = t 2 [b] t 1 > t 2 [c] t 1 2 [d] t 1 = √ 2 t 2 Q.20 Two projectiles X and Y are thrown with speed and u and √ 3u acquired the same maximum height. If X is thrown at an angle of 60 0 with the horizontal, then angle of projection for Y is [a] 75 0 [b] 60 0 [c] 45 0 [d] 30 0 Q.21 A grasshopper finds that he can jump a maximum horizontal distance of 1m. with what speed can he travel along the ground if he spends negligible time on the ground? [a] 9.8m/s [b] 4.42m/s [c] 2.21m/s [d] 3.16m/s Q.22 A monkey in a perch 20m high in a tree drops a coconut directly above your head as you run with a speed of 1.5m/s beneath the tree. How far behind you, does the coconut hit the ground? [a] 13.3m [b] 3m [c] strikes the head [d] 20m Q.23 In the above question, when should have the monkey thrown the coconut to hit your head? [a] 2 second earlier [b] 2 second later [c] 4 second earlier [d] can’t be found Q.24 A projectile is thrown with velocity v making an angle θ with the vertical gains maximum height H in time for which the particle remains in air, the time period is [a] [b] [c] [d] Q.25 A projectile is thrown with a velocity of ai +bj m/s. If the range of projectile is double the maximum height reached by it, [a] a=2b [b] b=4a [c] b=2a [d] b=a Q.26 Two stones are projected with the same velocity, in magnitude but making different angles with the horizontal. Their ranges are equal. If the angle of projection for one is 60 0 and maximum height is y 1 , then the maximum height of the other will be [a] 3y 1 [b] 2y 1 [c] y 1 /2 [d] y 1 /3 Q.27 The instantaneous height and horizontal distance x traveled by projectile are x=5t and y=5t-2t 2 . what is the acceleration if distance is measured in meters and time in seconds? [a] 10m/s 2 [b] 4m/s 2 [c] 6m/s 2 [d] 8m/s 2 Q.28 A body of mass m is projected with velocity v at an angle of 45 0 with the horizontal. The change in momentum at the end of the flight is [a] 2mv [b] mv [c] √ 2mv [d] 1.5mv Q.29 a body is projected such that its KE at highest point is 3/4 th of the initial KE. What is angle of projection with the horizontal? [a] 30 0 [b] 60 0 [c] 45 0 [d] 120 0 Q.30 A ball is thrown up at a given angle with the horizontal. Then the total change in momentum by the instant it returns to the ground is [a] mg x T [b] mgT/2 [c] mg x R [d] gT Q.31 A car is travelling with a velocity of 10km/h on a straight road. The driver of the car throws a parcel with a velocity of 10 √ 2 km/h when the car is passing a man standing on the side of the road. If the parcel is to reach the man, the direction of throw makes an following angle with the direction of the car [a] 135 0 [b]45 0 [c] tan -1 √ 2 [d] tan -1 [1/ √ 2] Q.32 A person aims a gun at a bird from the point, at a horizontal distance of 100m. if the gun can impact a speed of 500m/s to the bullet at what height above the bird must he aim his gun to hit the bird? [a] 10cm [b] 20cm [c] 50cm [d] 100cm Q.33 A ball is projected horizontally with a velocity of 4m/s. the velocity of the ball after 0.7 seconds is [a] 11m/s [b] 10m/s [c] 8m/s 3m/s Q.34 A particle is describing a circular path of radius 20m in 2 seconds. The average angular speed of the particle during 4 seconds is [a] 20 Π rad/s [b] 4 Π rad/s [c] Π rad/s [d] 2 Π rad/s Q.35 The ratio of angular speed of the minute hand to the hour hand of the watch is [a] 6:1 [b] 12;1 [c] 1:6 [d] 1:12 Q.36 To enable a particle to describe circular path what should be the angle between its velocity and acceleration? [a] 0 0 [b] 45 0 [c] 90 0 [d] 180 0 Q.37 The angular speed of the car increases from 600rpm to 1200rpm in 10 seconds. What is the angular acceleration of the car? [a] 600 rad/s 2 [b] 60 rad/s 2 [c] 60 Π rad/s 2 [d] 2 Π rad/s 2 Q.38 A point P moves in a circular path of radius r with uniform speed v. C is the center of the circle and AB is the diameter. The angular velocity of P about A and C is in the ratio [a] 1:1 [b] 1:2 [c] 2:1 [d] 4;1 Q.39 A car is going around a circle of radius R 1 with constant speed. Another car is going around a circle of radius R 2 with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds will be [a] [R 1 /R 2 ] 1/2 [b][R 2 /R 1 ] 1/2 [c] 1:1 [d] R 1 /R 2 Q.40 A stone is tied to one end of 5m long string and whirled in a vertical circle. The minimum speed required just to cross the topmost position is [a] 5m/s [b] 7m/s [c] 57m/s [d] 75m/s Q.41 A particle is performing uniform circular motion has [a] radial velocity and radial acceleration [b] radial velocity and transverse acceleration [c] transverse velocity and radial acceleration [d] transverse velocity and transverse acceleration Q.42 What should be time taken by earth to move around its own axis so that the body on equator flies off [a] 24 hrs [b] 0.14 hrs [c] 1.4 hrs [d] 14 hrs Q.43 A car is moving with a speed of 30m/s on a circular track of radius 500m. its speed is increasing at the rate of 2m/s 2 . what is the acceleration of the car? [a] 2m/s 2 [b] 2.7ms 2 [c] 1.8m/s 2 [d] 9.8m/s 2 Q.44 The radius of the circular path of a particle doubled but its frequency of rotation remains constant. If the initial centripetal force be F, then the final value of centripetal force will be [a] F [b] F/2 [c] 4F [d] 2F Q.45 An electric fan has blades of length 30cm rotating at 120rpm, the acceleration of the point on the tip of the blade is [a] 1600m/s 2 [b] 47.4m/s 2 [c] 23.7m/s 2 [d] 50.55m/s 2

** Q.1 A particle is moving in a straight line with initial velocity u and retardation αv, where v is the velocity at any time t**

** [a] the particle will cover a total distance u/α**

** [b] the particle will come to rest after 1/α**

** [c] the particle will continue to move for a very long time**

** [d] the velocity of the particle will become u/2 after time 1/α**

** Q.2 A particle moves along the xaxis as x = u(t-1) ^{2} + a(t-3)^{3}**

** [a] initial velocity of the particle is u**

** [b] the acceleration of the particle is a**

** [c] the acceleration of the particle is 2a**

** [d] the particle is at the origin at time t=3 seconds**

** Q.3 A particle is projected vertically upwards**

** [a] the speed decreases uniformly with distance**

** [b] the speed decreases uniformly with time**

** [c] the KE decrease uniformly with time**

** [d] KE decreases uniformly with distance**

** Q.4 If an observer moves at constant speed along the line joining two stationary objects> he will the two objects**

** [a] have the same velocity**

** [b] have the same speed**

** [c] move in opposite directions**

** [d] move in the same direction.**

** Q.5 A particle is moving with uniform acceleration along a straight line AB. Its speed at A and B are 2m/s and 14m/s respectively. Then**

** [a] its speed at the midpoint is 10m/s**

** [b] its speed at point P such that AP:PB is 1:5 is 4m/s**

** [c] the time to go from A to mid point of AB is double to move from mid point to B**

** [d] none of the above.**

** Q.6 A body starting from rest is moving with uniform acceleration of 5m/s ^{2} for time 10s, and after that with uniform acceleration of 10m/s^{2} for 15s, then**

** [a] average acceleration of the body is 7.5m/s ^{2}**

** [b] the average acceleration is 8m/s ^{2}**

** [c] total distance covered is 1875m**

** [d] total distance covered is 2125m**

** Q.7 A particle moves first 10m in 2s and 20m in the next 3s and 30m in next 10s. which of the following statements are true for motion?**

** [a] the particle is moving with uniform velocity**

** [b] the average speed of the particle is 4m/s**

** [c] the particle is uniformly accelerated**

** [d] the particle has deceleration during the motion**

** Q.8 Suppose a and v denoted the acceleration and velocity vector if the body in one dimensional motion:**

** [a] speed must increase if a > 0**

** [b] speed must increase if v and a >0**

** [c] speed must decrease if a<0**

** [d] speed will decrease if v<0 and a>0**

** Q.9 The motion of the particle falling in the restive medium is given by dv/dt = A-Bv where A and B are constants. Then**

** [a] the initial acceleration of the body is A**

** [b] the velocity at which the acceleration becomes zero is A/B**

** [c] the velocity at any time t is A(1-e ^{-Bt})/B**

** [d] all the above are wrong**

** Q.10 The displacement of the particle depends upon time as x = αt ^{2} – βt^{3}**

** [a] the particle will come to rest after time t=2 ^{α}/3β**

** [b] the particle will return to the starting point after time α/β**

** [c] no net force acts on the particle at t=α/3β**

** [d] the initial velocity of the particle was zero but initial acceleration was not zero.**

** Q.11 A lead ball is dropped into a lake from a diving board 5m above the water. If it hits the water with certain velocity and sinks to the bottom with same constant velocity. It reaches the bottom 5s after it is dropped.**

** [a] the depth of the lake is 40m**

** [b] the depth of the lake is 50m**

** [c] the average velocity of the ball is 5m/s**

** [d] the average velocity of the ball is 9m/s**

** Q.12 A balloon starts rising from the ground with an acceleration of 2.5m/s ^{2}. after 4 seconds the stone is relased from the balloon. If g=10m/s^{2}. The stone will**

** [a] have displacement of 25m**

** [b] cover a total distance of 30m**

** [c] reach the ground in 3.2s**

** [d] begins to move down after it is released.**

** Q.13 Which of the following about distance are true? **

** [a] it can’t be negative**

** [b] it can be zero**

** [c] it can be lesser than the magnitude of the displacement**

** [d] it can never decrease with time**

** Q.14 A particle of mass m moves on the x axis as follows. It starts from rest t t=0 from the point x=0 and comes to rest at time t=1 at the point x=1. No other information is available about intermediate times. If α denotes acceleration, then**

** [a] α cannot remain positive for all values of time between 0 and 1**

** [b] **** cannot exceed 2 at any pont in its path**

** [c] **** must be **** 4 at some point on its path**

** [d] α must change sign during motion but no other assertion can be made**

** Q.15 A ball is dropped from the window of a train moving with uniform velocity. The ball will reach the ground following a**

** [a] parabolic path for the passenger**

** [b] parabolic path for man standing on the ground**

** [c] straight line path for the passenger**

** [d] none of these**

** Q.16 A particle starts moving along a straight line with velocity of 10m/s. after 5 seconds the distance of the particle from the starting point is 50m. which of the following statement is true about the motion of the particle is true?**

** [a] the motion may be with constant acceleration **

** [b] the motion may be with the constant velocity**

** [c] the motion may be continuously retarded**

** [d] motion may be first accelerated and then retarded**

** Q.17 A body is dropped from the top of the tower of height h. it covers a distance h/3 in last minute of its motion. If g=10m/s ^{2}, how much time does it take to reach the ground?**

** [a] 2 + √3s [b]2-√3 s**

** [c] 3+√6s [d] 3-√6 s**

** Q.18 A Car starting from rets has a constant acceleration a _{1} for time interval t_{1} during which it covers a distance s_{1}. In the next time interval t_{2} the car has retardation a_{2} and comes to rest after covering distance s_{2} in time t_{2}. the average speed of the car during the journey is given by**

** [a] a _{1}t_{1}/2 [b]a_{2}t_{2}/2**

** [c][a _{1}+a_{2}][t_{1}+t_{2}’4 [d]zero**

** Q.19 a man throws a stone vertically upwards with a speed of 20m/s from the top of the high rise building. Two seconds later, an identical stone is thrown vertically downwards with speed of 20m/s. then:**

** [a] the relative velocity between the two stones remains constant till one hits the ground**

** [b] both will have the same kinetic energy when they hit the ground**

** [c] the time interval between their hitting the ground is 2s**

** [d] if the collision with the ground is perfectly elastic both will rise to the same height above the ground**

** Q.20 An aeroplane flis along the straight line from A to B with speed V and back again with the same speed. If there is steady wind speed v. the distance between A and B is l**

** [a] total time for the round trip, if wind blows along the line AB is 2V/[V ^{2}-v^{2}]**

** [b] total time for round trip if the wind blows perpendicular to AB is 2V/[V ^{2}-v^{2}]**

** [c] total time for round trip is always increased by the presence of the wind**

** [d] total time for round trip depends on the direction of the trip**

** Q.21 A particle starts from origin with coordinates at time t=0 and moves in th e x-y plane with constant acceleration α in the y direction. Its equation of motion is y=βx ^{2}. its velocity component in the x direction is equal to**

** [a]variable [b] α/2β**

** [c]**** [d]**

** Projectile Motion**

** Q.1 A body is projected at an angle of 30 ^{0} to the horizontal with a speed of 30m/s. what is angle with the horizontal after 1.5 seconds?**

** [a] 0 ^{0} [b] 30^{0}**

** [c] 60 ^{0} [d] 90^{0}**

** Q.2 A projectile is thrown with the initial velocity of 50m/s. the maximum horizontal distance this projectile can travel is**

** [a] 64m [b] 128m**

** [c] 5m [d] 255m**

** Q.3 The range of projectile which is launched at an angle of 15 ^{0} with the horizontal is 1.5km. what is the range of projectile which is fired at an angle of 45^{0} with same speed?**

** [a] 1.5km [b] 3km**

** [c] 6km [d] 0.75km**

** Q.4 When air resistance is taken into account while dealing with the motion of the projectile which of the following properties shows an increase?**

** [a] range [b] maximum height**

** [c] speed with which it strikes the ground**

** [d] the angle at which the projectile hits the ground**

** Q.5 A ball rolls off the edge of the stairway with a horizontal velocity of magnitude 1.8m/s. the steps are 0.2m high and 0.2m wide. Which step will ball hit first?**

** [a] first [b] second**

** [c] third [d] fourth**

** Q.6 A hunter aims at the monkey sitting on a tree at considerable distance. At the instant he fires at it the monkey drops. Will the bullet hit the monkey?**

** [a] no [b] yes**

** [c] sometimes [d] never**

** Q.7 The angle of projection, which for which the horizontal range and maximum height are equal is**

** [a] 45 ^{0} [b] tan^{-1}[4]**

** [c] tan ^{-1}[0.25] [d] none of these**

** Q.8 The height y and the distance along horizontal traveled by projectile is given by y = 8t-5t ^{2} and x=6t. the velocity of projection is**

** [a] 8m/s [b] 6m/s**

** [c] 10m/s [d] can’t be found**

** Q.9 A body is projected at an angle of 30 ^{0} to the horizontal with kinetic energy E. the KE at the highest point is**

** [a] zero [b] E/4 **

** [c] E/2 [d] 3E/4**

** Q.10 In projectile motion the angle between the velocity and acceleration at the highest point is**

** [a] 45 ^{0}_{ }[b] 30^{0}**

** [c] 90 ^{0} [d] 0^{0}**

** Q.11 A man can throw a stone to maximum horizontal distance of 80m. the maximum height to which he can throw is**

** [a] 10m [b] 20m**

** [c] 30m [d] 40m**

** Q.12 A gun fired two bullets at 60 ^{0} and 30^{0} with horizontal. The bullets strike at same horizontal distance. The ratio of maximum heights in the two cases is**

** [a] 1:1 [b] 2;1**

** [c] 3:1 [d] 4:1**

** Q.13 Which of the following does not affect the maximum height attained by the projectile?**

** [a] acceleration of the projectile**

** [b] magnitude of the initial velocity**

** [c] mass of the projectile**

** [d] angle of projection**

** Q.14 In projectile motion, the velocity**

** [a] is never perpendicular to the acceleration**

** [b] is always perpendicular to the acceleration**

** [c] is perpendicular to acceleration at one instant only**

** [d] is perpendicular to acceleration at two instants only.**

** Q.15 A ball rolls off the top of the stairway with velocity um/s in horizontal direction. If the steps are h meters high and b meter wide, the ball will hit the edge of nth step where n is**

** [a] 2hu/gb ^{2} [b] 2hu^{2}/gb^{2}**

** [c] 2hu ^{2}/gb [c] hu^{2}/gb^{2}**

** Q.16 An arrow is projected into air. Its times of flight is 5 second and range 200m. what is maximum height reached by it?**

** [a] 31.25m [b] 24.5m**

** [c] 18.25m [d] 46.75m**

** Q.17 A ball is thrown from the ground with a velocity of 20√3 m/s making an angle of 60 ^{0} with the horizontal. The ball will be at the height of 40m from the ground after a time of**

** [a] √2 second [b] √3m/s**

** [c] 2 second [d] 3 seconds.**

** Q.18 A projectile of mass 100gm is fired with a velocity of 20m/s making an angle of 30 ^{0} with the horizontal. As it rises to the highest point of its path, its momentum changes by**

** [a] 1/2kgm/s [b] 1kgm/s**

** [c] 2kgm/s [d] none of these**

** Q.19 From certain height, two bodies are projected horizontally with velocities 10m/s and 20m/s. they will hit the ground in time t _{1} and t_{2} second., then**

** [a] t _{1} = t_{2} [b] t_{1} > t_{2}**

** [c] t _{1}< t_{2} [d] t_{1} = √2 t_{2}**

** Q.20 Two projectiles X and Y are thrown with speed and u and √3u acquired the same maximum height. If X is thrown at an angle of 60 ^{0} with the horizontal, then angle of projection for Y is**

** [a] 75 ^{0} [b] 60^{0}**

** [c] 45 ^{0} [d] 30^{0}**

** Q.21 A grasshopper finds that he can jump a maximum horizontal distance of 1m. with what speed can he travel along the ground if he spends negligible time on the ground?**

** [a] 9.8m/s [b] 4.42m/s**

** [c] 2.21m/s [d] 3.16m/s**

** Q.22 A monkey in a perch 20m high in a tree drops a coconut directly above your head as you run with a speed of 1.5m/s beneath the tree. How far behind you, does the coconut hit the ground?**

** [a] 13.3m [b] 3m**

** [c] strikes the head [d] 20m**

** Q.23 In the above question, when should have the monkey thrown the coconut to hit your head?**

** [a] 2 second earlier [b] 2 second later**

** [c] 4 second earlier [d] can’t be found**

** Q.24 A projectile is thrown with velocity v making an angle θ with the vertical gains maximum height H in time for which the particle remains in air, the time period is**

** [a] **** [b] **

** [c] **** [d] **

** Q.25 A projectile is thrown with a velocity of ai +bj m/s. If the range of projectile is double the maximum height reached by it,**

** [a] a=2b [b] b=4a**

** [c] b=2a [d] b=a**

** Q.26 Two stones are projected with the same velocity, in magnitude but making different angles with the horizontal. Their ranges are equal. If the angle of projection for one is 60 ^{0} and maximum height is y_{1}, then the maximum height of the other will be**

** [a] 3y _{1} [b] 2y_{1}**

** [c] y _{1}/2 [d] y_{1}/3**

** Q.27 The instantaneous height and horizontal distance x traveled by projectile are x=5t and y=5t-2t ^{2}. what is the acceleration if distance is measured in meters and time in seconds?**

** [a] 10m/s ^{2} [b] 4m/s^{2}**

** [c] 6m/s ^{2} [d] 8m/s^{2}**

** Q.28 A body of mass m is projected with velocity v at an angle of 45 ^{0} with the horizontal. The change in momentum at the end of the flight is**

** [a] 2mv [b] mv**

** [c] √2mv [d] 1.5mv**

** Q.29 a body is projected such that its KE at highest point is 3/4 ^{th} of the initial KE. What is angle of projection with the horizontal?**

** [a] 30 ^{0} [b] 60^{0}**

** [c] 45 ^{0} [d] 120^{0}**

** Q.30 A ball is thrown up at a given angle with the horizontal. Then the total change in momentum by the instant it returns to the ground is**

** [a] mg x T [b] mgT/2**

** [c] mg x R [d] gT**

** Q.31 A car is travelling with a velocity of 10km/h on a straight road. The driver of the car throws a parcel with a velocity of 10√2 km/h when the car is passing a man standing on the side of the road. If the parcel is to reach the man, the direction of throw makes an following angle with the direction of the car **

** [a] 135 ^{0}_{ }[b]45^{0}**

** [c] tan ^{-1}√2 [d] tan^{-1}[1/√2]**

** Q.32 A person aims a gun at a bird from the point, at a horizontal distance of 100m. if the gun can impact a speed of 500m/s to the bullet at what height above the bird must he aim his gun to hit the bird?**

** [a] 10cm [b] 20cm**

** [c] 50cm [d] 100cm**

** Q.33 A ball is projected horizontally with a velocity of 4m/s. the velocity of the ball after 0.7 seconds is**

** [a] 11m/s [b] 10m/s**

** [c] 8m/s 3m/s**

** Q.34 A particle is describing a circular path of radius 20m in 2 seconds. The average angular speed of the particle during 4 seconds is**

** [a] 20Π rad/s [b] 4 Π rad/s**

** [c] Π rad/s [d] 2Π rad/s**

** Q.35 The ratio of angular speed of the minute hand to the hour hand of the watch is**

** [a] 6:1 [b] 12;1**

** [c] 1:6 [d] 1:12**

** Q.36 To enable a particle to describe circular path what should be the angle between its velocity and acceleration?**

** [a] 0 ^{0} [b] 45^{0}**

** [c] 90 ^{0} [d] 180^{0}**

** Q.37 The angular speed of the car increases from 600rpm to 1200rpm in 10 seconds. What is the angular acceleration of the car?**

** [a] 600 rad/s ^{2} [b] 60 rad/s^{2}**

** [c] 60Π rad/s ^{2} [d] 2Π rad/s^{2}**

** Q.38 A point P moves in a circular path of radius r with uniform speed v. C is the center of the circle and AB is the diameter. The angular velocity of P about A and C is in the ratio**

** [a] 1:1 [b] 1:2**

** [c] 2:1 [d] 4;1**

** Q.39 A car is going around a circle of radius R _{1} with constant speed. Another car is going around a circle of radius R_{2} with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds will be**

** [a] [R _{1}/R_{2}]^{1/2} [b][R_{2}/R_{1}]^{1/2}**

** [c] 1:1 [d] R _{1}/R_{2}**

** Q.40 A stone is tied to one end of 5m long string and whirled in a vertical circle. The minimum speed required just to cross the topmost position is**

** [a] 5m/s [b] 7m/s**

** [c] 57m/s [d] 75m/s**

** Q.41 A particle is performing uniform circular motion has**

** [a] radial velocity and radial acceleration**

** [b] radial velocity and transverse acceleration**

** [c] transverse velocity and radial acceleration**

** [d] transverse velocity and transverse acceleration**

** Q.42 What should be time taken by earth to move around its own axis so that the body on equator flies off**

** [a] 24 hrs [b] 0.14 hrs**

** [c] 1.4 hrs [d] 14 hrs**

** Q.43 A car is moving with a speed of 30m/s on a circular track of radius 500m. its speed is increasing at the rate of 2m/s ^{2}. what is the acceleration of the car?**

** [a] 2m/s ^{2} [b] 2.7ms^{2}**

** [c] 1.8m/s ^{2} [d] 9.8m/s^{2}**

** Q.44 The radius of the circular path of a particle doubled but its frequency of rotation remains constant. If the initial centripetal force be F, then the final value of centripetal force will be**

** [a] F [b] F/2**

** [c] 4F [d] 2F**

** Q.45 An electric fan has blades of length 30cm rotating at 120rpm, the acceleration of the point on the tip of the blade is**

** [a] 1600m/s ^{2} [b] 47.4m/s^{2}**

** [c] 23.7m/s ^{2} [d] 50.55m/s^{2}**

## 1 Answers

_{1 }to v

_{2}, the particle traverses a distance d in time t ; show that d/t