Question

A body of mass $10\text{kg}$ moving with velocity of $10\text{m/s}$ hits another body of mass $30\text{kg}$ moving with velocity $3\text{m/s}$ in same direction. The co-efficient of restitution is $\frac{1}{4}$. The velocity of centre of mass after collision will be

• A. $20\text{m/s}$
• B. $40\text{m/s}$
• C. $\frac{19}{4}\text{m/s}$
• D. $\frac{23}{4}\text{m/s}$

Answer 1

The correct option is C $\frac{19}{4}\text{m/s}$

Before collision, $v_{cm}=\frac{\left(10\right)\left(10\right)+\left(30\right)\left(3\right)}{10+30}=\frac{19}{4}\text{m/s}$
Since no external force acts on system, velocity of centre of mass remains constant.
The correct option is (C)