Question

The kinetic energy of a body of mass $0.5kg$ and momentum $30kgm{s}^{-1}$ is ___ J.

• A. 1500
• B. 4500
• C. 900
• D. 450

Answer 1

The correct option is C. 900

Given: Momentum, $p=30kgm{s}^{-1},m=0.5kg$

Let $v$ be the velocity of the body.

We know kinetic energy, $K.E=\frac{1}{2}m{v}^2$ and momentum, $p=mv\Rightarrow v=\frac{p}{m}$

So by substituting the value of $v$ in the expression of K.E,

$K.E=\frac{1}{2}m\times {\left(\frac{p}{m}\right)}^2=\frac{p^2}{2m}$

$\therefore K.E=\frac{p^2}{2m}=\frac{{30}^2}{2\times 0.5}=900J$.