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

Options

A. `(2U)/(v)`
B. `(U)/(2v)`
C. `(2U)/(v^(2))`
D. `(U)/(2v^(2))`

Explanation

To solve the problem, we will use the principle of conservation of mechanical energy. Here are the steps to find the mass of the body:

### Step-by-Step Solution:

**Step 1: Understand the scenario**
- A body is falling under the influence of gravity and starts from rest. As it falls, it loses gravitational potential energy (U) and gains kinetic energy.

**Step 2: Write the conservation of energy equation**
- The total mechanical energy is conserved. Initially, the body has gravitational potential energy and no kinetic energy (since it starts from rest). As it falls, the potential energy decreases and is converted into kinetic energy.
- The equation can be expressed as:
\[ \text{Potential Energy lost} = \text{Kinetic Energy gained} \]
Thus,
\[ U = \frac{1}{2} m v^2 \]

**Step 3: Rearrange the equation to solve for mass (m)**
- From the equation \( U = \frac{1}{2} m v^2 \), we can isolate \( m \):
\[ m = \frac{2U}{v^2} \]

**Step 4: Write the final answer**
- The mass of the body is given by:
\[ m = \frac{2U}{v^2} \]

### Final Answer:
The mass of the body shall be \( m = \frac{2U}{v^2} \).

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