The masses of two bodies are in the ratio `1:6` and their velocities are in the ratio `3:2` Then their momentum will be in the ratio

Options

A. `2:3`
B. `2:1`
C. `4 :1`
D. `1:4`

Answer

To find the ratio of the momentum of two bodies given their mass and velocity ratios, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Ratios**:
- The mass ratio of the two bodies is given as \( m_1 : m_2 = 1 : 6 \).
- The velocity ratio of the two bodies is given as \( v_1 : v_2 = 3 : 2 \).

2. **Express the Masses and Velocities**:
- Let the mass of the first body \( m_1 = 1 \) unit and the mass of the second body \( m_2 = 6 \) units.
- Let the velocity of the first body \( v_1 = 3 \) units and the velocity of the second body \( v_2 = 2 \) units.

3. **Write the Formula for Momentum**:
- The momentum \( p \) of an object is given by the formula:
\[ p = m \times v \]
- Therefore, the momentum of the first body \( p_1 = m_1 \times v_1 \) and the momentum of the second body \( p_2 = m_2 \times v_2 \).

4. **Calculate the Momentums**:
- For the first body:
\[ p_1 = m_1 \times v_1 = 1 \times 3 = 3 \text{ units} \]
- For the second body:
\[ p_2 = m_2 \times v_2 = 6 \times 2 = 12 \text{ units} \]

5. **Find the Ratio of the Momentums**:
- The ratio of the momentums \( p_1 : p_2 \) is:
\[ p_1 : p_2 = 3 : 12 \]
- Simplifying this ratio:
\[ p_1 : p_2 = \frac{3}{12} = \frac{1}{4} \]

### Final Answer:
The ratio of the momentums \( p_1 : p_2 \) is \( 1 : 4 \).

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