If the kinetic energy of a body changes by 20%, then its momentum would change by

Options

A. 0.2
B. 0.24
C. 0.1
D. 44%.

Explanation

To solve the problem of how much the momentum of a body changes when its kinetic energy changes by 20%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Kinetic Energy and Momentum**:
The kinetic energy (KE) of a body is given by the formula:
\[ KE = \frac{P^2}{2m} \]
where \( P \) is the momentum and \( m \) is the mass of the body. From this, we can see that kinetic energy is directly proportional to the square of momentum:
\[ KE \propto P^2 \]

2. **Express Momentum in Terms of Kinetic Energy**:
From the relationship above, we can express momentum in terms of kinetic energy:
\[ P \propto \sqrt{KE} \]

3. **Define Initial and Final Kinetic Energy**:
Let the initial kinetic energy be \( K \). If the kinetic energy changes by 20%, the final kinetic energy \( K' \) can be expressed as:
\[ K' = K + 0.2K = 1.2K \]

4. **Calculate Initial and Final Momentum**:
Using the relationship \( P \propto \sqrt{KE} \):
- Initial momentum \( P_1 \) is proportional to \( \sqrt{K} \):
\[ P_1 = k \sqrt{K} \]
- Final momentum \( P_2 \) is proportional to \( \sqrt{K'} \):
\[ P_2 = k \sqrt{1.2K} = k \sqrt{1.2} \sqrt{K} \]

5. **Find the Change in Momentum**:
The change in momentum \( \Delta P \) can be calculated as:
\[ \Delta P = P_2 - P_1 = k \sqrt{1.2} \sqrt{K} - k \sqrt{K} \]
Factoring out \( k \sqrt{K} \):
\[ \Delta P = k \sqrt{K} (\sqrt{1.2} - 1) \]

6. **Calculate the Percentage Change in Momentum**:
The percentage change in momentum is given by:
\[ \text{Percentage Change} = \frac{\Delta P}{P_1} \times 100 \]
Substituting \( P_1 \):
\[ \text{Percentage Change} = \frac{k \sqrt{K} (\sqrt{1.2} - 1)}{k \sqrt{K}} \times 100 = (\sqrt{1.2} - 1) \times 100 \]

7. **Calculate \( \sqrt{1.2} \)**:
We can approximate \( \sqrt{1.2} \):
\[ \sqrt{1.2} \approx 1.095 \]
Therefore:
\[ \sqrt{1.2} - 1 \approx 0.095 \]

8. **Final Calculation**:
Thus, the percentage change in momentum is:
\[ \text{Percentage Change} \approx 0.095 \times 100 \approx 9.5\% \]

### Conclusion:
The momentum of the body changes by approximately **9.5%**, which can be rounded to **10%**.