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 find the velocity of the composite system formed by two bodies with masses \( m_1 \) and \( m_2 \) and velocities \( v_1 \) and \( v_2 \), we can follow these steps:

### Step 1: Understand the Conservation of Momentum
In a collision, the total momentum before the collision is equal to the total momentum after the collision. This is based on the principle of conservation of momentum.

### Step 2: Write the Expression for Initial Momentum
The initial momentum of the system before the collision can be expressed as:
\[ P_{\text{initial}} = m_1 v_1 + m_2 v_2 \]

### Step 3: Set Up the Equation for Final Momentum
After the collision, the two bodies stick together and move as a composite system with a combined mass of \( m_1 + m_2 \) and a final velocity \( V \). Therefore, the final momentum can be expressed as:
\[ P_{\text{final}} = (m_1 + m_2)V \]

### Step 4: Apply the Conservation of Momentum
According to the conservation of momentum, we have:
\[ P_{\text{initial}} = P_{\text{final}} \]
Substituting the expressions we wrote:
\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2)V \]

### Step 5: Solve for the Final Velocity \( V \)
We can rearrange the equation to solve for \( V \):
\[ V = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \]

### Step 6: Use the Given Condition
From the problem, we know that:
\[ m_1 v_1 + m_2 v_2 = 0 \]
This implies:
\[ V = \frac{0}{m_1 + m_2} = 0 \]

### Conclusion
Thus, the velocity of the composite system after the collision is:
\[ V = 0 \]