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 v 1 ​ , in the direction of the bullet. Find the velocity of the bullet after the collision.

Explanation

To solve the problem, we will use the principle of conservation of momentum. The momentum before the collision must equal the momentum after the collision since there are no external forces acting on the system.

### Step-by-Step Solution:

1. **Identify Initial Momentum**:
The initial momentum of the system is due to the bullet only, as the ball is at rest.
\[
\text{Initial Momentum} = m \cdot v
...