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 1: Understand the relationship between momentum and velocity
The momentum \( p \) of a particle is defined as:
\[ p = mv \]
where \( m \) is the mass of the particle and \( v \) is its velocity.

### Step 2: Solve for velocity
We can rearrange the equation to find the velocity \( v \):
\[ v = \frac{p}{m} \]

### Step 3: Write the formula for kinetic energy
The kinetic energy \( KE \) of a particle is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]

### Step 4: Substitute the expression for velocity into the kinetic energy formula
Now, we substitute \( v = \frac{p}{m} \) into the kinetic energy formula:
\[ KE = \frac{1}{2} m \left(\frac{p}{m}\right)^2 \]

### Step 5: Simplify the expression
Now we simplify the expression:
\[ KE = \frac{1}{2} m \cdot \frac{p^2}{m^2} \]
This simplifies to:
\[ KE = \frac{p^2}{2m} \]

### Conclusion
Thus, the kinetic energy of the particle in terms of its momentum is:
\[ KE = \frac{p^2}{2m} \]