Question

A body of mass m moving with velocity $v$ makes a head on collision with another body of mass $2m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is

• A. $ \frac{1}{2} $ of its initial kinetic energy
• B. $ \frac{1}{9} $ of its initial kinetic energy
• C. $ \frac{8}{9} $ of its initial kinetic energy
• D. $ \frac{1}{4} $ of its initial kinetic energy

Answer 1

Answer: (C)

Final velocity of first body in collision
$v_{1}=\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) u_{1}+\left(\frac{2 m_{2}}{m_{1}+m_{2}}\right) u_{2}$
$v_{1}=\left(\frac{m-2 m}{m +2 m}\right) u_{1}+\left(\frac{2 \times 2 m}{m+2 m}\right) \times u_{2}$
$v_{1}=-\frac{v}{3}\left(\because u_{2}=0\right)$
Initial kinetic energy $=\frac{1}{2} m v^{2}$
Kinetic energy after collision is given by
$=\frac{1}{2} m\left(\frac{v}{3}\right)^{2}=\frac{1}{2} m \frac{v^{2}}{9}$
Change in kinetic energy
$=\frac{1}{2} m\left(v^{2}-\frac{v^{2}}{9}\right)$
$=\frac{8}{9}\left(\frac{1}{2} m v^{2}\right)=\frac{8}{9}$ (initial kinetic energy)