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)

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

Answer 2

Loss of kinetic energy of the colliding body

$\frac{\Delta K}{K} = 1 - \left( \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \right)^{2} = 1 - \left( \frac{m - 2m}{m + 2m} \right)^{2} = 1 - \left( \frac{1}{3} \right)^{2}\Delta K = \left( 1 - \frac{1}{9} \right)K = \frac{8}{9}K$

∴ Loss of kinetic energy is $\frac{8}{9}$ of its initial kinetic energy.