A body is falling under gravity. When it loses a gravitational potential energy by U, its speed is v. The mass of the body shall be

The correct option is 2U/v².

Step-by-step Derivation:

According to the law of conservation of energy, when a body falls freely under gravity, its loss in gravitational potential energy is converted entirely into a gain in kinetic energy, assuming air resistance is negligible.

Let the mass of the body be $m$ and its speed be $v$ after losing potential energy.

The gain in kinetic energy (KE) of the body is given by the formula:
$\text{Kinetic Energy}=\frac{1}{2}m{v}^2$

Since the loss in gravitational potential energy is $U$, we can equate the two energies:
$U=\frac{1}{2}m{v}^2$

To find the mass $m$ of the body, we rearrange the terms in the equation:
$2U=m{v}^2$

Now, dividing both sides by $v^2$, we get:
$m=\frac{2U}{v^2}$

Therefore, the mass of the body is $\frac{2U}{v^2}$, which corresponds to the option 2U/v².