Question

A body of mass $m$ with velocity $v$ makes a head-on elastic collision with another body of mass $3m$ at rest. The loss of kinetic energy of colliding body of mass $\left(m\right)$ is:

• A. $Zero$
• B. $\frac{1}{2}$ of its initial $K.E$.
• C. $\frac{\epsilon }{g}$ of its initial $K.E$.
• D. $\frac{3}{4}$ of its initial $K.E$.

Answer 1

The correct option is D $\frac{3}{4}$ of its initial $K.E$.

by conservation of momentum

$mv=(3+1)v_f$

$v_f=\frac{v}{4}$

loss in kinetic energy=$\frac{m{v}^2}{2}-\frac{4m(\frac{v}{4}{)}^2}{2}=\frac{3m{v}^2}{8}=\frac{3}{4}K{E}_i$