The momentum of a body is p and its kinetic energy is E. Its momentum becomes 2p. Its kinetic energy will be

Options

A. `(E )/(2)`
B. 3E
C. 2E
D. 4E

Explanation

To solve the problem, we need to understand the relationship between momentum and kinetic energy. Let's break it down step by step.

### Step 1: Understand the given quantities
- Initial momentum \( p \)
- Initial kinetic energy \( E \)
- Final momentum \( 2p \)

### Step 2: Recall the relationship between momentum and kinetic energy
The relationship between momentum \( p \) and kinetic energy \( E \) is given by the formula:
\[ E = \frac{p^2}{2m} \]
where \( m \) is the mass of the body.

### Step 3: Calculate the initial kinetic energy
Using the formula, we can express the initial kinetic energy in terms of momentum:
\[ E = \frac{p^2}{2m} \]

### Step 4: Calculate the final kinetic energy when momentum is \( 2p \)
Now, we need to find the final kinetic energy when the momentum becomes \( 2p \). We can substitute \( 2p \) into the kinetic energy formula:
\[ E' = \frac{(2p)^2}{2m} \]

### Step 5: Simplify the expression for final kinetic energy
Calculating \( (2p)^2 \):
\[ E' = \frac{4p^2}{2m} \]
This simplifies to:
\[ E' = 2 \cdot \frac{p^2}{2m} = 2E \]

### Step 6: Conclusion
Thus, the final kinetic energy \( E' \) when the momentum is \( 2p \) is:
\[ E' = 2E \]

### Final Answer
The final kinetic energy will be \( 2E \).

---