Question

A body of mass 20 gms is moving with a certain velocity. It collides with another body of mass 80gm at rest. The collision is perfectly inelastic. Find the ratio of the kinetic energies before and after collision of the system.

• A. 2 : 1
• B. 4 : 1
• C. 5 : 1
• D. 3 : 2

Answer 1

The correct option is C 5 : 1

Let $V$ be the velocity of the bodies after collision.
By using momentum conservation for inelastic collision, we get,
$m_1{u}_1+m_2{u}_2=(m_1+m_2)V$
$\Rightarrow V=\frac{m_1{u}_1+m_2{u}_2}{m_1+m_2}$
But $m_1=20$gm$,m_2=80$gm$,u_2=0$cm/s
$\Rightarrow V=\frac{20u_1+80\left(0\right)}{20+80}=\frac{u_1}{5}$
$K.E{.}_{Before}=\frac{1}{2}\times 20\times {u_1}^2=10{u_1}^2$
$K.E{.}_{After}=\frac{1}{2}\times (20+80)\times \frac{u_1^2}{25}=2u_1^2$
$\frac{K.E{.}_{Before}}{K.E{.}_{After}}=5$