If the linear momentum is increased by 50%, then KE will be increased by :

Options

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

Explanation

To solve the problem of how the kinetic energy (KE) changes when the linear momentum (P) is increased by 50%, we can follow these steps:

### Step-by-Step Solution:

1. **Define Initial Variables**:
Let the initial linear momentum be \( P \) and the initial kinetic energy be \( K \).

2. **Calculate Final Momentum**:
The problem states that the linear momentum is increased by 50%. Therefore, the final momentum \( P_f \) can be calculated as:
\[ P_f = P + 0.5P = 1.5P \]

3. **Relate Momentum and Kinetic Energy**:
We know the relationship between momentum and kinetic energy:
\[ P = \sqrt{2mK} \]
where \( m \) is the mass of the object. We can express the kinetic energy in terms of momentum:
\[ K = \frac{P^2}{2m} \]

4. **Calculate Final Kinetic Energy**:
Substitute \( P_f \) into the kinetic energy formula to find the final kinetic energy \( K_f \):
\[ K_f = \frac{(P_f)^2}{2m} = \frac{(1.5P)^2}{2m} = \frac{2.25P^2}{2m} = 1.125 \cdot \frac{P^2}{2m} = 1.125K \]

5. **Calculate Change in Kinetic Energy**:
The change in kinetic energy \( \Delta K \) can be calculated as:
\[ \Delta K = K_f - K = 1.125K - K = 0.125K \]

6. **Calculate the Fractional Increase in Kinetic Energy**:
To find the fractional increase in kinetic energy, we take the change in kinetic energy divided by the initial kinetic energy:
\[ \text{Fractional Increase} = \frac{\Delta K}{K} = \frac{0.125K}{K} = 0.125 \]

7. **Final Result**:
The kinetic energy increases by a factor of \( 1.125 \) or \( 12.5\% \).