Question

A body of mass $m$ has a momentum $p$. What is its kinetic energy?

• A. $\frac{p^2}{2m}$
• B. $\frac{p^2}{m}$
• C. $\frac{p^2}{2}$
• D. $\frac{p}{m^2}$

Answer 1

The correct option is A $\frac{p^2}{2m}$

Kinetic energy, $K.E.=\frac{1}{2}m{v}^2...\left(i\right)$
Let the speed of the body be $v$.
Momentum, $p=mv$
$v=\frac{p}{m}...\left(ii\right)$
Substituting the value of $v$ from equation (ii) in equation (i), we get:
$K.E.=\frac{1}{2}m{\left(\frac{p}{m}\right)}^2$
$K.E.=\frac{p^2}{2m}$