Question

The momentum $P$ and kinetic energy $E$ of a body of mass $m$ are related as:

• A. $P=\sqrt{2mE}$
• B. $P=\frac{1}{2}mE$
• C. $P=\frac{2m}{E}$
• D. $P=2mE$

Answer 1

The correct option is A $P=\sqrt{2mE}$

Lets take,
$m=$ mass of a body
$v=$ velocity of body
We know that kinetic energy is given by the formula, $E=\frac{1}{2}m{v}^2...\left(i\right)$

The momentum is given by the formula, $P=mv...\left(ii\right)$

In equation $\left(i\right)$, multiply and divide by $m$(mass) we get,

$E=\frac{1}{2}m{v}^2\times \frac{m}{m}=\frac{P^2}{2m}$ as, $(P=mv)$

$\Rightarrow P^2=2mE$

$P=\sqrt{2mE}$,

Hence option A is the correct answer.