Question

A body falls freely under gravity. Its velocity is $v$ when it has lost a potential energy of $U$. The mass of the body is

• A. $\frac{2U}{v^2}$
• B. $\frac{U}{v^2}$
• C. $\frac{U}{2v^2}$
• D. $v\times U$

Answer 1

The correct option is A

$\frac{2U}{v^2}$

Step 1: Given data

Velocity of the body is $v$

Loss of potential energy by the body is $U$

Step 2: Finding the mass of the body

Equating loss of potential energy with a gain of kinetic energy, we get

$$\begin{gathered} E_p=E_k \\ U=\frac{1}{2}m{v}^2 \\ m=\frac{2U}{v^2} \end{gathered}$$

Thus, the mass of the body is $\frac{2U}{v^2}.$

Hence, option (a) is correct.