A body of mass m moving with a constant velocity v hits another body of the same mass moving with the same velocity v but in the opposite direction and sticks to it. The velocity of the compound body after collision is

Options

A. V
B. 2V
C. v/2
D. 0

Answer

To solve the problem, we will use the principle of conservation of momentum. The momentum before the collision must equal the momentum after the collision.

### Step-by-Step Solution:

1. **Identify the masses and velocities:**
- Let the mass of the first body be \( m_1 = m \) and its initial velocity \( u_1 = v \).
- Let the mass of the second body be \( m_2 = m \) and its initial velocity \( u_2 = -v \) (negative because it is in the opposite direction).

2. **Write the expression for total momentum before the collision:**
- The total momentum before the collision is given by:
\[ \text{Total Momentum} = m_1 u_1 + m_2 u_2 = m \cdot v + m \cdot (-v) = mv - mv = 0 \]

3. **Apply the conservation of momentum:**
- According to the conservation of momentum, the total momentum before the collision equals the total momentum after the collision. Let \( V \) be the velocity of the combined mass after the collision.
- The total momentum after the collision is:
\[ \text{Total Momentum After} = (m_1 + m_2) V = (m + m) V = 2mV \]

4. **Set the total momentum before equal to the total momentum after:**
- From the conservation of momentum, we have:
\[ 0 = 2mV \]

5. **Solve for the final velocity \( V \):**
- Since \( 2m \) is not zero (mass cannot be zero), we can divide both sides by \( 2m \):
\[ V = 0 \]

### Final Answer:
The velocity of the compound body after the collision is \( V = 0 \).

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