# Collision

## A bullet of mass 20 g pieces through a plate of mass M1 = 1 kg and then comes to rest Inside a second plate of mass M2 = 2.98 kg as shown in the figure. The plates are on a smooth horizontal surface and bullet moves along the surface. It is found that the two plates. Initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is in between M1 and M2 .

Q: A bullet of mass 20 g pieces through a plate of mass M1 = 1 kg and then comes to rest Inside a second plate of mass M2 = 2.98 kg as shown in the figure. The plates are on a smooth horizontal surface and bullet moves along the surface. It is found that the two plates. Initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is in between M1 and M2 . Neglect any loss of material of the plates.

(a) 30 %

(b) 25 %

(c) 35 %

(d) 22.5 %

Ans: (b)

## A ball of mass m is projected with speed u into the barrel of a spring gun of mass M initially at rest on a frictionless surface. The mass m sticks in the barrel at the point of maximum compression of the spring. No energy is lost in friction. What fraction of the initial kinetic energy of the ball is stored in the spring?

Q: A ball of mass m is projected with speed u into the barrel of a spring gun of mass M initially at rest on a frictionless surface. The mass m sticks in the barrel at the point of maximum compression of the spring. No energy is lost in friction. What fraction of the initial kinetic energy of the ball is stored in the spring ?

(a) $\displaystyle \frac{m}{\sqrt{2} (M + m)}$

(b) $\displaystyle \frac{M}{\sqrt{2} (M + m)}$

(c) $\displaystyle \frac{m}{(M + m)}$

(d) $\displaystyle \frac{M}{(M + m)}$

Ans: (d)

## Two balls B1 and B2 having but unknown masses collide. B1 is initially at rest and B2 has a speed u. After collision, B2 has a speed u/2 and moves at right angles to its original motion. Find the direction (with respect to initial of B2) in which ball B1 moves after collision.

Q: Two balls B1 and B2 having but unknown masses collide. B1 is initially at rest and B2 has a speed u. After collision, B2 has a speed u/2 and moves at right angles to its original motion. Find the direction (with respect to initial of B2 ) in which ball B1 moves after collision.

(a) tan-1 (1/2)

(b) tan-1(2)

(c) tan-1(1/4)

(d) tan-1(4)

Ans: (a)

## A ball is projected with initial velocity u at Angle Ɵ with horizontal Then, horizontal displacement covered by the ball as it collides third time with the ground would be

Q: A ball is projected with initial velocity u at Angle Ɵ with horizontal Then, horizontal displacement covered by the ball as it collides third time with the ground would be (coefficient of restitution is e)

(a) $\displaystyle (1 + e) \frac{u^2 sin⁡2\theta}{g}$

(b) $\displaystyle (1 + e + e^2 ) \frac{u^2 sin⁡2\theta}{2 g}$

(c) $\displaystyle e \frac{u^2 sin⁡2\theta}{g}$

(d) $\displaystyle (1 + e + e^2) \frac{u^2 sin⁡2\theta}{g}$

Ans: (d)

## A sphere moving with velocity v strikes elastically with a wall moving towards the sphere with velocity u. If the mass of the wall is infinitely large, the work done by the wall during collision will be

Q: A sphere moving with velocity v strikes elastically with a wall moving towards the sphere with velocity u. If the mass of the wall is infinitely large, the work done by the wall during collision will be

(a) mu (u + v)

(b) 2 mu(u + v)

(c) (2/3) mu(u + v)

(d) (3/2) mu (u + v)

Ans: (b)