Introduction to Collision

Q. A ball A of mass m falls under gravity from a height h and strikes another ball B of mass m which is supported at rest on a spring of stiffness k. Assume perfect elastic impact. Immediately after the impact

1. The velocity of ball A is $\frac{1}{2}\sqrt{2gh}$
2. The velocity of ball A is Zero
3. The velocity of both balls is $\frac{1}{2}\sqrt{2gh}$
4. None of the above

Q. A bullet of mass m travels at a very high velocity V (as shown in the figure) and gets embedded inside the block of mass M initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance s along the floor. Assuming $\mu$ to be the coefficient of kinetic friction between the block and the floor and g the acceleration due to gravity what is the velocity V of the bullet?

1. $\frac{M+m}{m}\sqrt{2\mu gs}$
2. $\frac{M-m}{m}\sqrt{2\mu gs}$
3. $\frac{\mu (M+m)}{m}\sqrt{2\mu gs}$
4. $\frac{M}{m}\sqrt{2\mu gs}$

Q. The coefficient of restitution of a perfectly plastic impact is

1. 0
2. 1
3. 2
4. $\infty$

Q. During inelastic collision of two particles, which one of the following is conserved?

1. Total linear momentum only
2. Total kinetic energy only
3. Both linear momentum and kinetic energy
4. Neither linear momentum nor kinetic energy

Q. A ball of mass 3 kg moving with a velocity of $4\frac{m}{s}$ undergoes a perfectly-elastic direct-central impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value(s) of m is/are

1. 1 kg only
2. 1 kg, 9 kg
3. 1 kg, 6 kg
4. 6 kg only

Q. A tennis ball dropped from rest onto a cement floor rebounds $\frac{8}{10}$ of the height through which it fell. Neglecting air resistance, determine the coefficient of restitution.

1. 0.8
2. 0.895
3. 0.75
4. 0.5

Q. A mass $m_1$ of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass $m_2$ of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

1. 0.6
2. 0.1
3. 0.01
4. 0

Q. A bullet of mass $m_1=20gm$ fired horizontally with a velocity of $v=200m/s$ hits a wooden block of mass $m_2=500$ gm (take $g=9.8m/s^2$) resting on a horizontal plane as shown in the figure and the bullet remains embedded in the block after the impact. If the coefficient of friction between the surface in contact remains constant at 0.3, the distance the block will move before coming to rest is

1. 5.03 m
2. 10.06 m
3. 20.12 m
4. 100 m

Q. A bullet of mass m having a horizontal velocity of 500 m/s hits a stationary block of mass 6.15 kg. The block breaks into two parts viz. Q (mass of 3 kg) and R (mass of 3.15 kg) with the bullet embedded in R. The parts Q and R travel in the direction of initial velocity of the bullet. If the velocity of Q is 3 m/s and the velocity of R is 5 m/s the massof the bullet m is

1. 5 kg
2. 0.5kg
3. 0.05 kg
4. 0.005 kg

Q. A ball of mass 1.0 kg. moving with a veloity of 2 m/s collides directly with a stationary ball of mass 2 kg. If the first ball comes to rest after collision the velocity of the second ball after impact will be

1. 0 m/s
2. 0.5 m/s
3. 1.0 m/s
4. 1.5 m/s

Q. Two blocks shown in figure have equal masses. The surface of A is smooth while that of B has a friction coefficient of 0.10 with the floor. Block A is moving at a speed of 10 m/s towards B which is kept at rest. The distance travelled by block B if the collision is perfectly elastic is? $Assumeg=10m/s^2$.

1. 100 m
2. 200 m
3. 50 m
4. 25 m

Q. A mass $m_1$ with velocity $v_1$ impacts with a mass $m_2$ at rest. After the impact, the mass $m_1$ comes to rest. Then the coefficient of restitution e should be

1. $e=\frac{m_1}{m_1+m_2}$
2. $e=\frac{m_2}{m_1+m_2}$
3. $e=\frac{m_1}{m_2}$
4. $e=\frac{m_2}{m_1}$

Q. A body P while moving rectilinearly with velocity $V_o$ collides directly with another body Q, which is at rest, as shown below. Assuming both the bodies have the same mass and the collision is elastic, the velocities of the bodies after the collisions, measured positive towards right, are

1. $V_P=-V_o/2,V_Q=V_o/2$
2. $V_P=V_o/2,V_Q=V_o/2$
3. $V_P=0,V_Q=V_o/2$
4. $V_P=0,V_Q=V_o$

Q. Match 4 correct pairs between List-I and List-II for questions. No credit will be given for partially correct matching .
List-I
A. Collision of particles
B. Stability
C. Satellite motion
D. Spinning top
List-II
1. Euler's equation of motion
2. Minimum kinetic energy
3. Minimum potential energy
4. Impulse momentum principle

1. 1 3 5 1
2. 2 4 3 5
3. 4 3 2 5
4. 4 3 1 5

Q. A block of mass 5 kg moves up on a smooth inclined plane with a velocity of 10 m/s in the direction shown. A bullet of mass 60 g travelling at 500 m/s strikes the block centrally and gets embedded in it. The velocity of the block and embedded bullet in m/s immediately after the impact is

1. 12.34 at 30${}^{\circ }$
2. 13.84 at 51.78${}^{\circ }$
3. 13.84 at 30 ${}^{\circ }$
4. 15.62 at 78 ${}^{\circ }$

Q.

When a stationary rifle fires a bullet, the KE of the rifle + billet system increases to conserve the momentum. From where this energy is coming from? Or in this situation does the energy conservation law don’t hold good.