Two bodies having masses `m_(1)` and `m_(2)` and velocities `v_(1)` and `v_(2)` colide and form a composite system. If `m_(1)v_(1) + m_(2)v_(2) = 0(m_(1) ne m_(2)`. The velocity of composite system will be

Options

A. `v_(1)-v_(2)`
B. `v_(1) + v_(2)`
C. `(v_(1) + v_(2))/2`
D. zero

Explanation

To solve the problem, we need to determine the velocity of the composite system formed by two colliding bodies with given masses and velocities.

### Step-by-Step Solution:

1. **Understand the Given Information**:
We have two bodies with masses \( m_1 \) and \( m_2 \), and their respective velocities \( v_1 \) and \( v_2 \). It is given that:
\[ m_1 v_1 + m_2 v_2 = 0 \]

2. **Determine the Velocity of the Center of Mass**:
The velocity of the center of mass (V) of a system of particles is given by the formula:
\[ V = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \]

3. **Substitute the Given Condition**:
Since we know that \( m_1 v_1 + m_2 v_2 = 0 \), we can substitute this into the equation for the velocity of the center of mass:
\[ V = \frac{0}{m_1 + m_2} \]

4. **Simplify the Expression**:
This simplifies to:
\[ V = 0 \]

5. **Conclusion**:
Since there are no external forces acting on the system, the velocity of the center of mass remains constant. Therefore, the velocity of the composite system after the collision will also be:
\[ V = 0 \]

### Final Answer:
The velocity of the composite system will be \( 0 \).

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