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

Options

A. 1
B. 1.5
C. `sqrt(300%)`
D. `175%`

Explanation

To solve the problem, we need to determine the percentage change in momentum when the kinetic energy of a body is increased by 300%. Here’s a step-by-step solution:

### Step 1: Understand the initial kinetic energy
Let the initial kinetic energy (KE_initial) be denoted as \( k \).

### Step 2: Calculate the final kinetic energy
If the kinetic energy is increased by 300%, the final kinetic energy (KE_final) can be calculated as follows:
\[ \text{KE_final} = \text{KE_initial} + 300\% \text{ of KE_initial} = k + 3k = 4k \]

### Step 3: Relate kinetic energy to momentum
The momentum \( p \) of a body is related to its kinetic energy by the formula:
\[ p = \sqrt{2 \times m \times \text{KE}} \]
where \( m \) is the mass of the body.

### Step 4: Calculate initial momentum
Using the initial kinetic energy:
\[ p_{\text{initial}} = \sqrt{2 \times m \times k} \]

### Step 5: Calculate final momentum
Using the final kinetic energy:
\[ p_{\text{final}} = \sqrt{2 \times m \times 4k} = \sqrt{8mk} = 2\sqrt{2mk} \]

### Step 6: Express final momentum in terms of initial momentum
We can express the final momentum in terms of the initial momentum:
\[ p_{\text{final}} = 2 \cdot p_{\text{initial}} \]

### Step 7: Calculate the change in momentum
The change in momentum (\( \Delta p \)) is given by:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} = 2p_{\text{initial}} - p_{\text{initial}} = p_{\text{initial}} \]

### Step 8: Calculate the percentage change in momentum
The percentage change in momentum can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\Delta p}{p_{\text{initial}}} \right) \times 100 = \left( \frac{p_{\text{initial}}}{p_{\text{initial}}} \right) \times 100 = 100\% \]

### Final Answer
The percentage change in momentum is **100%**.

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