Question

How is kinetic energy ($K$) of a body of mass $m$, related to its momentum ($p$)?

• A. $K=\frac{p^2}{2m}$
• B. $K=\frac{p^2}{4m}$
• C. $K=2m{p}^2$
• D. $K=4m{p}^2$

Answer 1

Answer: (A)

$K=\frac{p^2}{2m}$

Kinetic energy of the moving body $K=\frac{1}{2}m{v}^2$ .....(1)

where $m$ is the mass of the body and $v$ is the velocity of the body.

Multiplying and divide $m$ in equation (1) we get $K=\frac{(mv{)}^2}{2m}$ .....(2)

Momentum of the body $p=mv$

Putting this in equation (2), we get $K=\frac{p^2}{2m}$