A particle of mass m has momentum p. Its kinetic energy will be

Options

A. mp
B. `p^(2)m`
C. `(p^(2)/(m)`
D. `p^(2)/(2m)`

Explanation

To find the kinetic energy of a particle with mass \( m \) and momentum \( p \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The momentum \( p \) of a particle is defined as:
\[ p = mv \]
where \( v \) is the velocity of the particle.

2. **Express Kinetic Energy**:
- The kinetic energy \( K \) of a particle is given by:
\[ K = \frac{1}{2}mv^2 \]

3. **Relate Velocity to Momentum**:
- From the momentum equation \( p = mv \), we can express the velocity \( v \) in terms of momentum:
\[ v = \frac{p}{m} \]

4. **Substitute Velocity into Kinetic Energy**:
- Now, substitute the expression for \( v \) into the kinetic energy formula:
\[ K = \frac{1}{2}m\left(\frac{p}{m}\right)^2 \]

5. **Simplify the Expression**:
- Simplifying the equation:
\[ K = \frac{1}{2}m \cdot \frac{p^2}{m^2} = \frac{p^2}{2m} \]

6. **Final Result**:
- Therefore, the kinetic energy \( K \) of the particle in terms of its momentum \( p \) is:
\[ K = \frac{p^2}{2m} \]

### Conclusion:
The kinetic energy of a particle with mass \( m \) and momentum \( p \) is given by:
\[ K = \frac{p^2}{2m} \]