Question

A bullet of mass m and velocity a is fired into a large block of wood of mass M. The final velocity of the system is ________.

• A. $\frac{m}{m+M}a$
• B. $\frac{M}{m+M}a$
• C. $\frac{m+M}{m}a$
• D. $\frac{m+M}{M}a$

Hint:

In perfectly inelastic collisions, the masses combine into one unit.

Answer 1

The Correct Option is A

Step 1: Concept
Conservation of Linear Momentum: Initial Momentum = Final Momentum.
Step 2: Analysis
Initial momentum = $(m \times a) + (M \times 0) = ma$. Final state: The bullet is inside the block, so they move together as a single system of mass $(m+M)$.
Step 3: Calculation
$ma = (m + M) \cdot v_{final}$. $v_{final} = \frac{m}{m+M}a$.
Step 4: Conclusion
Hence, the final velocity is $\frac{m}{m+M}a$.
Final Answer:(A)