Question

For a moving particle (mass $m$, velocity $v$) having a momentum $p$, which one of the following correctly describes the kinetic energy of the particle?

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

Answer 1

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

The kinetic energy of the particle is $K=\frac{1}{2}m{v}^2$
As momentum, $p=mv$ or $p^2=m^2{v}^2$ or $v^2=\frac{p^2}{m^2}$
$\therefore K=\frac{1}{2}m\left(\frac{p^2}{m^2}\right)=\frac{p^2}{2m}$.