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
$v_1=\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1+\left(\frac{2m_2}{m_1+m_2}\right)u_2$
$v_1=\left(\frac{m-2m}{m+2m}\right)u_1+\left(\frac{2\times 2m}{m+2m}\right)\times u_2$
$v_1=-\frac{v}{3}\left(\because u_2=0\right)$
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)