A body of mass $m$ moving with velocity $v$ collides head on with another body of mass $2m $ which is initially at rest. The ratio of K.E. of colliding body before and after collision will be
A body of mass $m$ moving with velocity $v$ collides head on with another body of mass $2m $ which is initially at rest. The ratio of K.E. of colliding body before and after collision will be
$1:1$
$2:1$
$4:1$
$9:1$
A body of mass $m$ moving with velocity $v$ collides head on with another body of mass $2m $ which is initially at rest. The ratio of K.E. of colliding body before and after collision will be
K.E. of colliding body before collision $ = \frac{1}{2}m{v^2}$
After collision its velocity becomes
$v' = \frac{{({m_1} - {m_2})}}{{({m_1} + {m_2})}}v = \frac{m}{{3m}}v = \frac{v}{3}$
K.E. after collision$\frac{1}{2}mv{'^2}$$ = \frac{1}{2}\frac{{m{v^2}}}{9}$
Ratio of kinetic energy =$\frac{{{\rm{K}}{\rm{.E}}{{\rm{.}}_{{\rm{before}}}}}}{{{\rm{K}}{\rm{.E}}{{\rm{.}}_{{\rm{after}}}}}} = \frac{{\frac{1}{2}m{v^2}}}{{\frac{1}{2}\frac{{m{v^2}}}{9}}} = 9:1$