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

Options

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

Explanation

To find the mass of a body falling under gravity when it loses a gravitational potential energy \( U \) and has a speed \( v \), we can use the principle of conservation of energy. Here’s the step-by-step solution:

### Step 1: Understand the Energy Transformation
When a body falls under the influence of gravity, it loses gravitational potential energy (U) and gains kinetic energy (KE). According to the law of conservation of energy, the loss in potential energy is equal to the gain in kinetic energy.

### Step 2: Write the Equation for Energy Conservation
The change in potential energy (\( \Delta U \)) is equal to the change in kinetic energy (\( \Delta KE \)):
\[ \Delta U = \Delta KE \]
Given that the body loses potential energy \( U \), we can express this as:
\[ U = \Delta KE \]

### Step 3: Express Kinetic Energy in Terms of Mass and Velocity
The kinetic energy (\( KE \)) of a body is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is the mass of the body
- \( v \) is the speed of the body

### Step 4: Set Up the Equation
Since the body loses potential energy \( U \) and this is equal to the kinetic energy gained, we can write:
\[ U = \frac{1}{2} mv^2 \]

### Step 5: Solve for Mass \( m \)
To find the mass \( m \), we rearrange the equation:
\[ m = \frac{2U}{v^2} \]

### Final Answer
Thus, the mass of the body is:
\[ m = \frac{2U}{v^2} \]

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