If the mass of a body is increased by 20%, then the momentum of body remains same, if the velocity approximately ______.

Options

A. decreases by 17%
B. increases by 17%
C. decreases by 83%
D. increases by 32%

Explanation

To solve the problem, we need to understand the relationship between mass, velocity, and momentum.

### Step-by-Step Solution:

1. **Understanding Momentum**:
Momentum (P) is defined as the product of mass (m) and velocity (v):
\[ P = m \times v \]

2. **Initial Conditions**:
Let the initial mass be \( m_1 \) and the initial velocity be \( v_1 \). Therefore, the initial momentum \( P_1 \) can be expressed as:
\[ P_1 = m_1 \times v_1 \]

3. **Change in Mass**:
The problem states that the mass of the body is increased by 20%. Thus, the new mass \( m_2 \) can be calculated as:
\[ m_2 = m_1 + 0.20 \times m_1 = 1.20 \times m_1 \]

4. **Final Momentum**:
We want the final momentum \( P_2 \) to remain the same as the initial momentum \( P_1 \). Therefore, we can write:
\[ P_2 = m_2 \times v_2 \]
Setting \( P_1 \) equal to \( P_2 \):
\[ m_1 \times v_1 = m_2 \times v_2 \]

5. **Substituting for \( m_2 \)**:
Substitute \( m_2 \) into the equation:
\[ m_1 \times v_1 = (1.20 \times m_1) \times v_2 \]

6. **Canceling \( m_1 \)**:
Since \( m_1 \) is common on both sides, we can cancel it (assuming \( m_1 \neq 0 \)):
\[ v_1 = 1.20 \times v_2 \]

7. **Solving for \( v_2 \)**:
Rearranging the equation gives:
\[ v_2 = \frac{v_1}{1.20} \]
This can be simplified to:
\[ v_2 = \frac{100}{120} \times v_1 = 0.8333 \times v_1 \]

8. **Calculating Percentage**:
To express \( v_2 \) as a percentage of \( v_1 \):
\[ v_2 = 83.33\% \text{ of } v_1 \]
This indicates that the velocity has decreased.

9. **Finding the Decrease**:
To find the percentage decrease:
\[ \text{Percentage decrease} = 100\% - 83.33\% = 16.67\% \approx 17\% \]

### Final Answer:
The velocity must be decreased by approximately **17%** for the momentum to remain the same.