An explosion blows a rock into three parts. Two parts go off at right angles to each other . These two are `1 kg` first part moving with a velocity of `12 ms^(-1) and 2 kg` second part moving with a velocity of `8 ms^(-1)`. If the third part flies off with a velocity of `4 ms^(-1)`. Its mass would be

Options

A. `5 kg`
B. `7 kg`
C. `17 kg`
D. `3kg`

Explanation

To solve the problem, we will apply the principle of conservation of momentum. The total momentum before the explosion must equal the total momentum after the explosion.

### Step-by-Step Solution:

1. **Identify the Masses and Velocities of the Parts:**
- Mass of the first part, \( m_1 = 1 \, \text{kg} \) with velocity \( v_1 = 12 \, \text{m/s} \) (moving vertically).
- Mass of the second part, \( m_2 = 2 \, \text{kg} \) with velocity \( v_2 = 8 \, \text{m/s} \) (moving horizontally).
- Mass of the third part, \( m_3 \) (unknown) with velocity \( v_3 = 4 \, \text{m/s} \) (unknown direction).
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