Question

A bullet of mass m moving at a speed v hits a ball of mass M kept at rest. A small part having mass m breaks from the ball and sticks to the bullet. The remaining ball is found to move at a speed v₁ in the direction of the bullet. Find the velocity of the bullet after the collision.

Answer 1

Given:
The mass of bullet moving with speed v is m.
The mass of the ball is M and it is at rest.

m' is the fractional mass of the ball that sticks with the bullet.
The remaining mass of the ball moves with the velocity v₁.

Let v₂ be the final velocity of the bullet plus fractional mass system.

On applying the law of conservation of momentum, we get:

mv + 0 = (m' + m)v₂ + (M − m') v₁

$\Rightarrow v_2=\frac{mv-(M-m\text{'})v_1}{m+m\text{'}}$
Therefore, the velocity of the bullet after the collision is $\frac{mv-(M-m\text{'})v_1}{m+m\text{'}}$.