Q.1. Where will be the centre of mass on combining two masses m and M (M>m)

(1) Towards m   (2) Towards M    (3) Between m and M    (4) Anywhere

  

Q.2.Two objects of masses 200 gm and 500gm possess velocities \( 10\hat{i} \) m/s and \(3\hat{i}+5\hat{j} \)m/s respectively .The velocity of their centre of mass in m/s is

(1) \(5\hat{i}-25\hat{j}\)     (2) \( \frac{5}{7}\hat{i}-25\hat{j}\)     (3) \(5\hat{i}+\frac{25}{7}\hat{j}\)    (4) \(25\hat{i}-\frac{5}{7}\hat{j}\)

Q.3.In the HCl molecule, the separation between the nuclei of the two atoms is about1.27 Å (1 Å = 10–10 m). The approximate location of the centre of mass of the molecule from hydrogenis (assuming the chlorine atom to be about 35.5 times massive as hydrogen)

(1) 1 Å           (2) 2.5 Å         (3) 1.24 Å         (4) 1.5 Å

Q.4. Four particle of masses m, 2m, 3m and 4m are arranged at the corners of a parallelogram with each sideequal to a and one of the angle between two adjacent sides is 60°. The parallelogram lies in the x-y plane

with mass m at the origin and 4m on the x-axis. The centre of mass of the arrangement will be located at

(1) \((\frac{\sqrt(3)}{2}a, 0.95a)\)     (2) \((0.95a, \frac{\sqrt{3}}{4}a )\)    (3) \((\frac{3a}{4}, \frac{a}{2})\)     (4) \((\frac{a}{2}, \frac{3a}{4})\)

Q.5 If a bomb is thrown at a certain angle with the horizontal and after exploding on the way the different fragments move in different directions then the centre of mass

(1) Would move along the same parabolic path

(2) Would move along a horizontal path

(3) Would move along a vertical line

(4) None of these

Q.6 Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of centre of mass of the system is

(1) Zero            (2) v            (3) 1.5v          (4) 3v

Q.7 Two point masses m and M are separated by a distance L. The distance of the centre of mass of the system from m is

(1)\( L(m/M)\)    (2) \(L(M/m)\)    (3) \(L (\frac{M}{m+M})\)    (4) \(L(\frac{m}{m+M})\)

Q.8 Three identical spheres, each of mass 1 kg are placed touching each other with their centres on a straight line. Their centres are marked K, L and M respectively. The distance of centre of mass of the system from K is

(1) \( \frac{KL+KM+LM}{3}\)    (2) \(\frac{KL+KM}{3}\)    (3)  \(\frac{KL+LM}{3}\)    (4) \(\frac{KM+LM}{3}\)

Q.9 Two particles of masses 1 kg and 3 kg move towards each other under their mutual force of attraction.No other force acts on them. When the relative velocity of approach of the two particles is 2m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s, the

velocity of the centre of mass is

(1) 0.5 m/s       (2) 0.75 m/s     (3) 1.25 m/s     (4) Zero

Q.10 A uniform metal disc of radius R is taken and out of it a disc of diameter R is cut off from the end. The centre of mass of the remaining part will be:

(1) \(\frac{R}{4} \)from the centre    (2) \(\frac{R}{3}\) from the centre    (3) \(\frac{R}{5}\)from the centre    (4)\(\frac{R}{6}\) from the centre

Q.11 The coordinate of the centre of mass of a system as shown in figure :–

                                                 

(1) \((\frac{a}{3}, 0)\)    (2) \((\frac{a}{2},\frac{a}{2})\)    (3) \((\frac{a}{3},\frac{a}{3})\)    (4)  \((0,\frac{a}{3})\) 

Q.12 The centre of mass a system of particles does not depend on :

(1) masses of the particles

(2) forces on the partices

(3) position of the particles

(4) relative distance between the particles

Q.13 The centre of mass of a system of two particles divides the distance between them

(1) In inverse ratio of square of masses of particles

(2) In direct ratio of square of masses of particles

(3) In inverse ratio of masses of particles

(4) In direct ratio of masses of particles

Q.14 All the particles of a body are situated at a distance R from the origin. The distance of the centre of

mass of the body from the origin is

(1) \(= R\)       (2)\(\leq R\)         (3)\( > R \)       (4) \(\geq R\)

Q.15 A uniform solid cone of height 40 cm is shown in figure. The distance of centre of mass of the cone from point B (centre of the base) is :

                          

(1) 20 cm       (2) 10/3 cm       (3) 20/3 cm        (4) 10 cm

Q.16 In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10–10 m). The approximate location of the centre of mass of the molecule, distance from hydrogen atom assuming the chlorine atom to be about 35.5 times massive as hydrogen is

(1) 1Å         (2) 2.5 Å       (3) 1.24 Å         (4) 1.5 Å

Q.17 The centre of mass of triangle shown in figure has coordinates

                                       

(1) \(x = \frac{h}{2}, y = \frac{b}{2} \)    (2) \(x = \frac{b}{2}, y = \frac{h}{2} \)    (3)  \(x = \frac{b}{3}, y = \frac{h}{3} \)    (4) \(x = \frac{h}{3}, y = \frac{b}{3} \)

Q.18 A uniform square plate ABCD has a mass of 10 kg. If two point masses of 3 kg each are placed at the corners C and D as shown in the adjoining figure, then the centre of mass shifts to the point which is lie on -

                                      

(1) OC                (2) OD                 (3) OY              (4) OX

Q.19 Two balls are thrown in air. The acceleration of the centre of mass of the two balls while in air (neglect air resistance)

(1) depends on the direction of the motion of the balls

(2) depends on the masses of the two balls

(3) depends on the speeds of the two balls

(4) is equal to g

Q.20.Two objects of masses 200 gm and 500gm possess velocities \( 10\hat{i} \) m/s and \(3\hat{i}+5\hat{j} \)m/s respectively .The velocity of their centre of mass in m/s is

(1) \(5\hat{i}-25\hat{j}\)    (2) \( \frac{5}{7}\hat{i}-25\hat{j}\)    (3) \(5\hat{i}+\frac{25}{7}\hat{j}\)    (4) \(25\hat{i}-\frac{5}{7}\hat{j}\)

Q.21 A body of mass 20 kg is moving with a velocity of 2v and another body of mass 10 kg is moving with velocity V along same direction . The velocity of their centre of mass is

(1) 5v/3       (2) 2v/3          (3) v         (4) Zero

Q.22 Two particles whose masses are 10 kg and 30 kg and their position vectors are \(\hat{i}+\hat{j}+\hat{k}\) and \(-\hat{i}-\hat{j}-\hat{k} \) respectively would have the centre of mass at -

(1) \(- \frac{(\hat{i}+\hat{j}+\hat{k})}{2}\)    (2) \(\frac{(\hat{i}+\hat{j}+\hat{k})}{2}\)   (3)  \(- \frac{(\hat{i}+\hat{j}+\hat{k})}{4}\)  (4) \(\frac{(\hat{i}+\hat{j}+\hat{k})}{4}\)

                            MOMENTUM & COLLISION

Q.23 Three particles with masses 10, 20 and 40gm are moving with velocities \(10\hat{i}\), \(\hat{j}\) and \(10\hat{k}\) m/sec respectively. If due to some interaction the first particle comes to rest and the velocity of second  becomes \((3\hat{i}+4\hat{j})\)  m/sec. then the velocity of third particle after the interaction is-

(1) \(\hat{i}+\hat{j}+5\hat{k}\)    (2) \(\hat{j}+10\hat{k}\)    (3)\(\hat{i}+\hat{j}+10\hat{k}\)    (4) \(\hat{i}+3\hat{j}+10\hat{k}\)

MOMENTUM

Q.24 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 speed v each, in mutually perpendicular directions. The total energy released in the process of explosion is-

(1) 3mv² /2       (2) mv²      (3) 4mv²        (4) 2mv² 

Q.25 A bullet of mass m is being fired from a stationary gun of mass M. If the velocity of the bullet is v, the velocity of the gun is-

(1) \(\frac{Mv}{m+M}\)    (2)  \(\frac{mv}{M}\)    (3)  \(\frac{(M+m)v}{M}\)    (4) \(\frac{M+m}{Mv}\)

Q.26 A bomb explodes in air in two equal fragments. If one of the fragments is moving vertically upwards with velocity v₀ , then the other fragment is moving-

(1) Vertically up with velocity v₀     (2) Vertically downwards with velocity v₀     (3) In any arbitrary direction     (4) None of these

Q.27 Two particles with equal kinetic energies are having masses in the ratio of 1 : 2. Then linear momenta will be in the ratio-

(1) 1        (2) 4           (3) 0.707           (4) 2

Q.28 Three particles A, B and C of equal mass move with equal speeds v along the medians of an equilateral triangle as shown in the figure. They collide at the centroid G of the triangle. After collision A comes to rest, B retraces its path with speed v. The velocity of C is-

(1)\(\vec{v}\) direction \(\vec{G} A\)

(2) \(\vec{2}v \) &  direction GA                                

(3) 2v, direction \(\vec{GB}\)

(4) \(\vec{v}, \) & direction \(\vec{BG}\)

Q.29 A space craft of mass M is travelling in space with velocity v. It then breaks up into two parts such that the smaller part m comes to the rest, then the velocity of the remaining part is-

(1) \(\frac{Mv}{M-m}\)   (2) \(\frac{Mv}{M+m}\)   (3) \(\frac{mv}{M-m}\)    (4)\(\frac{Mv}{m}\)

Q.30 A bomb at rest has mass 60 kg. It explodes and a fragment of 40 kg has kinetic energy 96 joule. Then kinetic energy of other fragment is-

(1) 180 J      (2) 190 J       (3) 182 J         (4) 192 J

Q.31 Consider the following two statements-

(A) Linear momentum of a system of particle is zero

(B) kinetic energy of a system of particles is zero. Then

(1) A does not imply B but B implies A

(2) A implies B and B implies A

(3) A does not imply B & B does not imply A

(4) A implies B but B does not imply A

Q.32 A radioactive nucleus initially at rest decays by emitting an electron and neutrino at right angles to one another. The momentum of the electron is 3.2 × 10^–23 kg-m/sec. and that of the neutrino is 6.4 × 10^–23 kg-m/sec. The direction of the recoiling nucleus with that of the electron motion is-

(1) tan^–1 (0.5)             (2) tan^–1 (2)        (3) \(\pi\) – tan^–1 (2)     (4) \(\frac{\pi}{2}\) + tan^-1(2)

Q.33 An isolated particle of mass m is moving in a horizontal plane (x-y) along the x-axis at a certain height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An instant later the

smaller fragment is at y = + 15 cm. The larger fragment at this instant is at

(1) y = – 5cm    (2) y = + 20cm    (3) y = + 5cm    (4) y = – 20cm

Q.34 A cannon ball is fired with a velocity 200m/sec at an angle of 60º with the horizontal. At the highest point of its flight, it explodes into 3 equal fragments, one going vertically upwards with a velocity 100m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity

(1) 100 m/sec in the horizontal direction

(2) 300m/sec in the horizontal direction

(3) 300 m/sec in a direction making an angle of 60º with the horizontal

(4) 200 m/sec in a direction making an angle of 60º with the horizontal

Q.35 A body of mass m collides against a wall with the velocity v and rebounds with the same speed. The change in momentum of body is

                                     

(1) – 2 mv        (2) mv         (3) – mv       (4) 0

Q.36 A bomb at rest explodes into two parts of masses m₁ and m₂ . If the momentums of the two parts be p₁ and p₂ , then their kinetic energies will be in the ratio of-

(1) m₁ / m₂     (2) m₂ / m₁    (3) p₁ / p₂        (4) p₂ / p₁

Q.37 A pulley fixed to the ceiling carries a string with blocks of masses m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be :

(1) zero     (2) \(-\frac{g}{4}\)     (3) \( \frac{g}{2}\)       (4) \(- \frac{g}{2}\)

 

COLLISION

Q.38 In the elastic collision of objects

(1) Only momentum remains constant 

(2) Only kinetic energy remains constant

(3) Both remains constant                      

(4) None of these

Q.39 A body of mass 2kg makes an elastic collision with another body at rest and continues to move in the original direction with one fourth of its original speed. The mass of the second body which collides with the first body is

 (1) 2 kg      (2) 1.2 kg      (3) 3 kg      (4) 1.5 kg

Q.40 In above question if transfer kinetic energy to B is maximum then

 (1) M_B >> M_A     (2) M_B << M_A       (3) M_A =  M_B      (4) Can not be predicted as information is incomplete

Q.41 A particle of mass m moving with a velocity V makes a head on elastic collision with another particle of same mass initially at rest. The velocity of the first particle after the collision will be

 (1) V              (2) – V              (3) – 2V           (4) Zero

Q.42 A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, their velocities after the collision will be, respectively

 (1) 6 m/s, 12 m/s     (2) 12 m/s, 6 m/s     (3) 12 m/s, 10 m/s     (4) 12 m/s, 25 m/s

Q.43 A light particle moving horizontally with a speed of 12 m/s strikes a very heavy block moving in the same direction at 10 m/s. The collision is one-dimensional and elastic. After the collision, the particle will         

(1) Move at 2 m/s in its original direction

(2) Move at 8 m/s in its original direction

(3) Move at 8 m/s opposite to its original direction
(4) Move at 12 m/s opposite to its original direction

A sphere A moving with a speed u and rotating with an angular velocity \(\omega\) , makes a head- on elastic collision with an identical stationary sphere B. There is no friction between the surfaces of A and B. Disregard gravity. 

(1) A will stop moving but continue to rotate with an angular velocity \(\omega\) 

(2) A will come to rest and stop rotating

(3) B will move with a sped u without rotating 

(4) B will move with a speed u and rotate with an angular velocity \(\omega\) 

Q.45 A neutron moving with a velocity 'v' and kinetic energy 'E' collides perfectly elastically head on with the nucleus of an atom of mass number 'A' at rest. The energy received by the nucleus and the total energy of the system are related by

(1) \(\frac{4A}{(A+1)^{2}}\)   \(\left    (2) ( \frac{A-1}{A+1}^{2} \right)\)    (3) \(\frac{(A+1)}{4A^{2}}\)    (4) \(\left ( \frac{A+1}{A-1}^{2} \right)\)

Q.46 An object A collides head on elastically with a stationary object B. The object B will recoil with maximum speed if (e = 1) 

(1) M_B >> M_A   (2) M_B << M_A   (3) M_A = M_B   (4) Can not be predicted due to incomplete data

Q.47 In above question the transfer momentum to B will be maximum if

 (1) M_B >> M_A   (2) M_B << M_A   (3) M_A = M_B   (4) Can not be predicted as information is incomplete

Q.48 A ball collides elastically with another ball of the same mass. The collision is oblique and initially one of the body was at rest. After the collision, the two balls move with same speeds. What will be the angle between the initial and final velocities of the colliding ball

 (1) 30°        (2) 45°         (3) 60°        (4) 90°

Q.49 A billiard ball moving at a speed 2m/s strikes an identical ball initially at rest, at a glancing blow. After the collision one ball is found to be moving at a speed of 1m/s at o 60 with the original line of motion. The velocity of the other ball shall be

(1) (3) m /s ^{1/ 2} at 30° to the original direction  

(2) 1m/s at o 60° to the original direction 

(3) (3) m /s ^{1/ 2} at o 60° to the original direction 

(4) 1m/s at o 30° to the original direction

 Q.50 A particle of mass m collides perfectly elastically with another particle of mass M = 2m . If the incident particle deflected by 90°. The heavy mass will make an angle with the initial direction of m equal to

 (1) 15°        (2) 30°        (3) 45°        (4) 60° 

Q.51 The co-efficient of restitution depends upon 

(1) The masses of the colliding bodies 

(2) The direction of motion of the colliding bodies 

(3) The inclination between the colliding bodies 

(4) The materials of the colliding bodies 

Q.52 Inelastic collision is the 

(1) Collision of ideal molecules with the walls of the container 

(2) Collision of electron and positron to annihilate each other 

(3) Collision of two rigid solid spheres lying on a frictionless table 

(4) Scattering of \(\alpha \)-particles with the nucleus of gold atom 

Q.53 A ball is dropped from height 10m. Ball is embedded in sand 1m and stops, then 

(1) Only momentum remains conserved 

(2) Only kinetic energy remains conserved 

(3) Both momentum and kinetic energy are conserved 

(4) Neither kinetic energy nor momentum is conserved 

Q.54 A ball is dropped from a height h. If the coefficient of restitution be e, then to what height will it rise after jumping twice from the ground

 (1) eh / 2        (2) 2eh        (3) eh        (4) e⁴h

Q.55 Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of 1 45 \(\sqrt{2}ms^{-1}\)  each, the velocity of their combined mass after collision is

(1) 1 45\(\sqrt{2}ms^{-1}\)    (2) 1 45\(\sqrt{2}ms^{-1}\)    (3) 1 90ms^-1 (4) 22.5 \(\sqrt{2}ms^{-1}\)   

Q.56 A body of 2kg mass and velocity 3m/s collides with a body of 1kg mass and moving oppositely with a velocity of 4m/sec. After collision both bodies stik and move with a common velocity. This velocity in m/s is

 (1) 1/ 4         (2) 1/ 3         (3) 2/3         (4) 3/4 

Q.57 A 50g bullet moving with a velocity of 1 10ms^-1 strikes a block of mass 950g at rest and gets embedded in it. The percentage loss in kinetic energy is 

(1) 100%         (2) 95%         (3) 5%         (4) 50% 

 

Q.58 Two pendulums each of length l are initially situated as shown in figure. The first pendulum is released and strikes the second. Assume that the collision is completely inelastic and neglect the mass of the string and any frictional effects. How high does the centre of mass rise after the collision

                                            

(1) \(d\left [ \frac{m_{1}}{\left (  m_{1}+m_{2}\right )} \right ]^{2}\)        (2)\(d\left [ \frac{m_{1}}{\left (  m_{1}+m_{2}\right )} \right ]\) 

(3) \(\frac{d(m_{1}+m_{2})^{2}}{m_{2}}\)          (4) \(d\left [ \frac{m_{2}}{\left (  m_{1}+m_{2}\right )} \right ]\) 

Q.59 A body of mass 2.9kg is suspended from a string of length 2.5m and is at rest. A bullet of mass 100g , moving horizontally with a speed of 1 150ms^-1 , strikes and sticks to it. What is the maximum angle made by the string with the vertical after the impact ( g =10 ms ^-2 ) 

(1) 30°         (2) 45°         (3) 60°         (4) 90°

  

EXERCISE-2

CENTRE OF MASS

Q.1 Two homogenous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is : (1) a          (2) 2a          (3) 3a          (4) none of these 

Q.2 A non–uniform thin rod of length L is placed along x-axis as such its one of ends at the origin. The linear mass density of rod is\(\lambda = \lambda_{0} \)x. The distance of centre of mass of rod from the origin is :

(1) L/2          (2) 2L/3            (3) L/4            (4) L/5 

Q.3 The centre of mass of the shaded portion of the disc is : (The mass is uniformly distributed in the shaded portion) :    

(1) \(\frac{R}{20}\)to the left of A      (2)\(\frac{R}{12}\)to the left of A      

 (3)\(\frac{R}{20}\)R to the right of A      (4)\(\frac{R}{12}\)R to the right of A

Q.4 Four particle of masses m, 2m, 3m and 4m are arranged at the corners of a parallelogram with each side equal to a and one of the angle between two adjacent sides is 60º. The parallelogram lies in the x-y plane with mass m at the origin and 4m on the x-axis. The centre of mass of the arrangement will be located at

(1)\(\left ( \frac{\sqrt{3}}{2}a,0.95a \right )\)       (2)\(\left ( 0.95a,\frac{\sqrt{3}}{4}a, \right )\)       (3)\(\left ( \frac{3a}{4},\frac{a}{2} \right)\)    (4)\(\left ( \frac{a}{2},\frac{3a}{4} \right)\)

Q.5 If linear density of a rod of length 3m varies as \(\lambda \) = 2 + x, then the position of the centre of gravity of the rod is

(1)\(\frac{7}{3}\)m        (2)\(\frac{12}{7}\)m        (3)\(\frac{10}{7}\)        (4)\(\frac{9}{7}\)m

Q.6 Two particles having mass ratio n : 1 are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is :

(1) (n – 1)² g      (2)\(\left ( \frac{n+1}{n-1} \right)^{2}\)g     (3)\(\left ( \frac{n-1}{n+1} \right)^{2}\)g     (4)\(\left ( \frac{n+1}{n-1} \right)\)g

Q.7 A uniform thin rod of mass M and Length L is standing vertically along the y-axis on a smooth horizontal surface, with its lower end at the origin (0,0). A slight disturbance at t = 0 causes the lower end to slip on the smooth surface along the positive x-axis, and the rod starts falling. The acceleration vector of centre of mass of the rod during its fall is : [\(\vec{R}\) is reaction from surface]

(1)\(\vec{a}_{CM}=\frac{M\vec{g}+\vec{R}}{M}\)   (2)\(\vec{a}_{CM}=\frac{M\vec{g}-\vec{R}}{M}\)   (3)\(\vec{a}_{CM}= M\vec{g}-\vec{R}\)   (4)None of these

Q.8 In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed it moves towards right. By the time the block reaches the right end of the tube then the displacement of the tube will be (where ‘R’ is mean radius of tube). Assume that the tube remains in vertical plane.

(1)\(\frac{2R}{\pi}\)        (2)\(\frac{4R}{\pi}\)       (3)\(\frac{R}{2}\)        (4)R

Q.9 A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of plank is M/3, the distance that the plank moves relative to the ground is : 

(1) 3L/4          (2) L/4          (3) 4L/5          (4) L/3

Q.10 Two  blocks A and B are connected by a massless string (shown in figure) A force of 30 N is applied on block B. The distance travelled by centre of mass in 2s starting from rest is :

(1) 1m          (2) 2m         (3) 3m         (4) none of these

Q.11 If the system is released, then the acceleration of the centre of mass of the system :

(1)\(\frac{3L}{4}\)         (2)\(\frac{L}{4}\)        (3)\(\frac{4L}{5}\)        (4)\(\frac{L}{3}\)

MOMENTUM

Q.13 A stationary body explodes into two fragments of masses m₁ and m₂ . If momentum of one fragment is p, the minimum energy of explosion is

(1)\(\frac{p^{2}}{2(m_{1}+m_{2})}\)     (2)\(\frac{p^{2}}{2\sqrt{m_{1}m_{2}}}\)     (3)\(\frac{p^{2}((m_{1}+m_{2})}{2(m_{1}m_{2})}\)      (4)\(\frac{p^{2}}{2(m_{1}-m_{2})}\)

Q.14 A train of mass M is moving on a circular track of radius 'R' with constant speed V. The length of the train is half of the perimeter of the track. The linear momentum of the train will be

(1) 0          (2) \(\frac{2MV}{\pi }\)          (3) MVR          (4) MV

Q.15 If the momentum of a body increases by 20%, the percentage increase in its kinetic energy is equal to : 

(1) 44       (2) 88        (3) 66        (4) 20 

Q.16 A man of mass 'm' climbs on a rope of length L suspended below a balloon of mass M. The balloon is stationary with respect to ground. If the man begins to climb up the rope at a speed v_rel (relative to rope). In what direction and with what speed (relative to ground) will the balloon move?

(1)downwards,\(\frac{mv_{rel}}{m+M}\)        (2)upwards,\(\frac{mv_{rel}}{m+M}\)    

(3)downwards,\(\frac{mv_{rel}}{M}\)      (4)downwards,\(\frac{(M+m)v_{rel}}{M}\)

Q.17 In the figure shown the initial velocity of boat (30 kg) + person (15 kg ) is 2 m/s. Find velocity of person w.r.t. boat so that velocity of boat will be 1 m/s in right (Neglect friction between boat and water)

(1) 3 m/s towards right           (2) 3 m/s towards left       

(3) 4 m/s towards right           (4) 4 m/s towards left

COLLISION

Q.18 In the figure shown the change in magnitude of momentum of the block when it comes to its initial position if the maximum compression of the spring is x₀ will be

(1)\(2\sqrt{km}\)  x₀       (2)\(\sqrt{km}\)x₀         (3) zero         (4) none of these

Q.19 When two bodies collide elastically, the force of interaction between them is :

 (1) conservative             (2) non–conservative    

(3) either conservative or non–conservative       (4) zero 

Q.20 During the head on collision of two masses 1 kg and 2 kg the maximum energy of deformation is \(\frac{100}{3}\) j. If before collision the masses are moving in the opposite direction, then their velocity of approach before the collision is : 

(1) 10 m/sec.        (2) 5 m/sec.       (3) 20 m/sec.      (4)10 \(\sqrt{2}\) m/sec.

Q.21 1 kg body explodes into three fragments. The ratio of their masses is 1 : 1 : 3. The fragments of same mass move perpendicular to each other with speed 30 ms–1, while the heavier part remains in the initial direction. The speed of heavier part is :

(1)\(\frac{10}{\sqrt{2}}\) ms^-1        (2)10\(\sqrt{2}\)ms^-1        (3)20\(\sqrt{2}\)ms^-1       (4)30\(\sqrt{2}\) ms^-1   

Q.22 A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The intial velocity of the shell is : 

(1) 100 ms^–1        (2) 80 ms^–1        (3) 40 ms^–1       (4) 120 ms^–1 

Q.23 A heavy nucleus at rest breaks into two fragments which fly off with velocities 8 : 1. The ratio of radii of the fragments is : 

(1) 1 : 2        (2) 1 : 4       (3) 4 : 1       (4) 2 : 1 

Q.24 A mass 'm' moves with a velocity 'v' and collides inelastically with another identical mass. After collision the Ist mass moves with velocity \(\frac{v}{\sqrt{3}}\) 3 v in a direction perpendicular to the initial direction of motion. Find the speed of the 2^nd mass after collision

(1)v         (2)\(\sqrt{3}v\)        (3)\(\frac{2}{\sqrt{3}}\)v         (4)\(\frac{v}{\sqrt{3}}\)

Q.25 A frame of mass 200 g when suspended from a massless spring extends it by 10 cm. A lump of clay of mass 200 g is dropped from rest on to the frame from a height of 30 cm as shown in figure. As a result, the speed of pan after the clay drops on it is :

(1)\(\sqrt{6}m/s\)        (2)6m/s        (3)\(\sqrt{3/2}m/s\)        (4)\(\sqrt{3}m/s\)

Q.26 A sphere of mass m moving horizontally with velocity v₀ collides against a pendulum bob of mass m. If the two masses stick together after the collision, then the maximum height attained is :

(1)\(\frac{vo^{2}}{2g}\)         (2)\(\frac{v_{o}^{2}}{4g}\)         (3)\(\frac{v_{o}^{2}}{6g}\)         (4)\(\frac{v_{o}^{2}}{8g}\)

Q.27 A 1 kg ball moving at 12 ms^-1 collides head-on a 2 kg ball moving in opposite direction with a speed of 24 ms^–1. If coefficient of restitution is 2/3, then :

(1) the respective velocities of the two balls after collision are–28 m s^–1 and – 4 m s^–1

(2) the respective velocities of the two balls after collision are in opposite directions

 (3) the energy lost in the collision is 1312 J 

(4) the energy gained in the collision is 1312 J 

Q.28 Two balls of same mass each m are moving with same velocities v on a smooth surface as shown in figure. If all collisions between the masses and with the wall are perfectly elastic, the possible number of collisions between the bodies and wall together is :

(1) 1           (2) 2           (3) 3          (4) infinity 

Q.29 A body of mass ‘m’ is dropped from a height of ‘h’. Simultaneously another body of mass 2m is thrown up vertically with such a velocity v that they collide at the height h/2. If the collision is perfectly inelastic, the velocity at the time of collision with the ground will be :

(1)\(\sqrt{\frac{5gh}{4}}\)        (2)\(\sqrt{gh}\)        (3)\(\sqrt{\frac{gh}{4}}\)        (4)\(\sqrt{\frac{10gh}{3}}\)

Q.30 Three blocks are initially placed as shown in the figure. Block A has mass m and initial velocity v to the right. Block B with mass m and block C with mass 4m are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block A is 

(1) 0.6v to the left      (2) 1.4v to the left      (3) v to the left      (4) 0.4v to the right 

Q.31 A ball is dropped from a height h. As it bounces off the floor, its speed is 80 percent of what it was just before it hit the floor. The ball will then rise to a height of most nearly 

(1) 0.80 h         (2) 0.75 h         (3) 0.64 h        (4) 0.50 h 

Q.32 A ball is dropped from height 5m. The time after which ball stops rebounding if coefficient of restitution between ball and ground e = 1/2, is 

(1) 1 sec          (2) 2 sec         (3) 3 sec         (4) infinite