Question

A bullet of mass \( m \) moving with velocity \( v \) is fired into a wooden block of mass \( M \). If the bullet remains embedded in the block, the final velocity of the system is

• A. \( \frac{v}{m(M+m)} \)
• B. \( \frac{m+M}{m} \)
• C. \( \frac{M+m}{m} v \)
• D. \( \frac{mv}{m+M} \)

Hint:

In inelastic collisions, momentum is conserved, but kinetic energy is not. Use conservation of momentum to find the final velocity.

Answer 1

The Correct Option is D

Step 1: Conservation of momentum.
Since the bullet remains embedded in the block, this is an inelastic collision. The total momentum before and after the collision must be conserved. The initial momentum of the system is \( mv \), and the final momentum is \( (m + M)v_f \). Thus, by conservation of momentum: \[ mv = (m + M) v_f \] Solving for \( v_f \), the final velocity of the system: \[ v_f = \frac{mv}{m + M} \]
Step 2: Conclusion.
Thus, the correct answer is (D) \( \frac{mv}{m+M} \).