Question

A particle of mass \(m\) collides with another stationary particle of mass \(M\). The particle of mass \(m\) stops just after collision. The coefficient of restitution is

• A. \( \dfrac{m+M}{m} \)
• B. \( \dfrac{m}{M} \)
• C. \( \dfrac{M}{m} \)
• D. \( \dfrac{M-m}{M+m} \)

Hint:

If one body comes to rest after collision, use momentum conservation first.

Answer 1

The Correct Option is B

Step 1: Definition of coefficient of restitution.
\[ e = \frac{\text{relative speed of separation}}{\text{relative speed of approach}} \]
Step 2: Using conservation of momentum.
Initial momentum:
\[ mu = Mv \Rightarrow v = \frac{m}{M}u \]
Step 3: Calculating coefficient of restitution.
Since particle of mass \(m\) stops after collision:
\[ e = \frac{v - 0}{u - 0} = \frac{v}{u} \]
Step 4: Substituting value of \(v\).
\[ e = \frac{m}{M} \]
Step 5: Conclusion.
The coefficient of restitution is \( \dfrac{m}{M} \).