Question

A body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2\, m$ 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)

$\frac{8}{9}$ of its initial kinetic energy

Answer 2

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 $=\frac{1}{2} m v_{1}^{2}$ Kinetic energy after collision is given by $=\frac{1}{2} m\left(-\frac{v}{3}\right)^{2}$ $=\frac{1}{2} m\left(\frac{v^{2}}{9}\right)$ Change in kinetic energy $=\frac{1}{2} m\left(v^{2}-\frac{v^{2}}{9}\right)$ $=\frac{8}{9}\left(\frac{1}{2} m v^{2}\right)$ $=\frac{8}{9} \times$ initial kinetic energy