If kinetic energy of a body is increased by 300%, then percentage change in momentum will be

Options

A. 1
B. 1.5
C. 2.65
D. 0.732

Answer

To solve the problem of determining the percentage change in momentum when the kinetic energy of a body is increased by 300%, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kinetic Energy Increase**:
- An increase of 300% in kinetic energy means that the new kinetic energy (K2) is 400% of the original kinetic energy (K1).
- Mathematically, if K1 is 100%, then K2 = K1 + 300% of K1 = 100% + 300% = 400%.

2. **Using the Relationship Between Kinetic Energy and Momentum**:
- The kinetic energy (K) of an object is related to its momentum (p) by the formula:
\[ K = \frac{p^2}{2m} \]
- Rearranging this gives us:
\[ p = \sqrt{2mK} \]

3. **Calculating Initial and Final Momentum**:
- Let the initial momentum (p1) correspond to the initial kinetic energy (K1 = 100%).
\[ p_1 = \sqrt{2m \cdot K_1} \]
- For the final momentum (p2) corresponding to the final kinetic energy (K2 = 400%):
\[ p_2 = \sqrt{2m \cdot K_2} = \sqrt{2m \cdot 4K_1} = 2\sqrt{2m \cdot K_1} = 2p_1 \]

4. **Finding the Change in Momentum**:
- The change in momentum (Δp) can be calculated as:
\[ \Delta p = p_2 - p_1 = 2p_1 - p_1 = p_1 \]

5. **Calculating the Percentage Change in Momentum**:
- The percentage change in momentum is given by:
\[ \text{Percentage Change} = \left(\frac{\Delta p}{p_1}\right) \times 100\% \]
- Substituting the values:
\[ \text{Percentage Change} = \left(\frac{p_1}{p_1}\right) \times 100\% = 100\% \]

### Final Answer:
The percentage change in momentum when the kinetic energy of the body is increased by 300% is **100%**.