If momentum of a certain body is increased by 50% then increase in the K.E. of the body will be

Options

A. 0.25
B. 0.5
C. 1
D. 1.25

Explanation

To solve the problem, we need to determine the increase in kinetic energy when the momentum of a body is increased by 50%.

### Step-by-Step Solution:

1. **Understanding Momentum and Kinetic Energy**:
- The momentum \( P \) of a body is given by the formula:
\[ P = mv \]
where \( m \) is the mass and \( v \) is the velocity of the body.
- The kinetic energy \( K \) is given by the formula:
\[ K = \frac{1}{2} mv^2 \]

2. **Expressing Kinetic Energy in Terms of Momentum**:
- We can express kinetic energy in terms of momentum:
\[ K = \frac{P^2}{2m} \]

3. **Calculating New Momentum**:
- If the momentum is increased by 50%, the new momentum \( P' \) is:
\[ P' = 1.5P \]

4. **Calculating New Kinetic Energy**:
- The new kinetic energy \( K' \) with the new momentum is:
\[ K' = \frac{(P')^2}{2m} = \frac{(1.5P)^2}{2m} \]
- Simplifying this, we get:
\[ K' = \frac{2.25P^2}{2m} = 1.125 \cdot \frac{P^2}{m} = 2.25K \]

5. **Finding the Increase in Kinetic Energy**:
- The increase in kinetic energy \( \Delta K \) is given by:
\[ \Delta K = K' - K = 2.25K - K = (2.25 - 1)K = 1.25K \]

6. **Expressing the Increase as a Percentage**:
- The increase in kinetic energy as a fraction of the original kinetic energy is:
\[ \text{Increase} = \frac{\Delta K}{K} = \frac{1.25K}{K} = 1.25 \]

### Final Answer:
The increase in kinetic energy of the body will be **125%** of the original kinetic energy.