KE of a body is increased by `44%.` What is the percent increse in the momentum ?

Options

A. `10%`
B. `20%`
C. `30%`
D. `44%`

Answer

To solve the problem of finding the percentage increase in momentum when the kinetic energy of a body is increased by 44%, 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. Rearranging gives us:
\[ p = \sqrt{2m \cdot KE} \]

2. **Define Initial and Final Kinetic Energy**:
Let the initial kinetic energy be \( KE_i \). According to the problem, the final kinetic energy \( KE_f \) is increased by 44%:
\[ KE_f = KE_i + 0.44 \cdot KE_i = 1.44 \cdot KE_i \]

3. **Calculate Initial and Final Momentum**:
Using the relationship between momentum and kinetic energy:
- Initial momentum \( p_i \):
\[ p_i = \sqrt{2m \cdot KE_i} \]
- Final momentum \( p_f \):
\[ p_f = \sqrt{2m \cdot KE_f} = \sqrt{2m \cdot (1.44 \cdot KE_i)} = \sqrt{1.44} \cdot \sqrt{2m \cdot KE_i} = \sqrt{1.44} \cdot p_i \]

4. **Calculate the Value of \( \sqrt{1.44} \)**:
\[ \sqrt{1.44} = 1.2 \]
Therefore, we have:
\[ p_f = 1.2 \cdot p_i \]

5. **Find the Percentage Increase in Momentum**:
The percentage increase in momentum is given by:
\[ \text{Percentage Increase} = \frac{p_f - p_i}{p_i} \times 100 \]
Substituting \( p_f \):
\[ \text{Percentage Increase} = \frac{(1.2 \cdot p_i) - p_i}{p_i} \times 100 = \frac{0.2 \cdot p_i}{p_i} \times 100 = 20\% \]

### Final Answer:
The percentage increase in momentum is **20%**.

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