Question

A body of mass $m$ moving with velocity $v$ makes a head on elastic collision with another body of mass $2m$ which in 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

The correct option is C $\frac{8}{9}$ of its initial kinetic energy

Conservation of momentum just before and after collision
$m_1{v}_1=m_1{v}_1^{\prime }+m_2{v}_2^{\prime }$

Conservation of kinetic energy
$0.5m_1{v}_1^2=0.5m_1{v_1^{\prime }}^2+0.5m_2{v_2^{\prime }}^2$

Solving these two gives
$v_1^{\prime }=\frac{m_1-m_2}{m_1+m_2}{v}_1=\frac{m-2m}{m+2m}v=-\frac{1}{3}v$

$\therefore$ KE after collision$=0.5m{\left(\frac{1}{3}v\right)}^2=\frac{0.5m{v}^2}{9}$

Kinetic energy transferred$=0.5m{v}^2-\frac{0.5m{v}^2}{9}=\frac{8}{9}\times 0.5m{v}^2$

Option C.