Question

A light and a heavy body have equal momentum. Which one has greater kinetic energy?

• A. The light body
• B. Both have equal K.E.
• C. The heavy body
• D. Data given is incomplete

Answer 1

The correct option is A The light body

Let $M_1<M_2$
Given $P_1=M_1{v}_1=M_2{v}_2=P_2$
Kinetic energy $K=\frac{P^2}{2M}$
$\frac{K_1}{K_2}=\frac{P_1^2}{P_2^2}\frac{M_2}{M_1}=\frac{M_2}{M_1}$
Since $M_1<M_2\Rightarrow K_1>K_2$
Hence, KE of lighter body is greater