A body of mass 2kg moving with a velocity of 3m/sec towards left collides head-on with a body of mass 3kg moving in opposite direction with a velocity 2m/sec. After collision the two bodies stick together and move with a common velocity which is :

Options

A. 5m/sec towards right
B. 12 m/sec towards right
C. 12/5 m/sec towards left
D. zero

Answer

To solve the problem step-by-step, we will use the principle of conservation of momentum.

### Step-by-Step Solution:

1. **Identify the masses and velocities of the bodies:**
- Mass of body 1 (m1) = 2 kg, moving left with velocity (v1) = -3 m/s (negative because it's to the left).
- Mass of body 2 (m2) = 3 kg, moving right with velocity (v2) = 2 m/s (positive because it's to the right).

2. **Write down the formula for momentum:**
- The momentum (p) of an object is given by the formula:
\[ p = m \cdot v \]
- Therefore, the total initial momentum (p_initial) before the collision is:
\[ p_{\text{initial}} = m_1 \cdot v_1 + m_2 \cdot v_2 \]

3. **Substitute the values into the momentum equation:**
- Substitute the known values:
\[ p_{\text{initial}} = (2 \, \text{kg} \cdot -3 \, \text{m/s}) + (3 \, \text{kg} \cdot 2 \, \text{m/s}) \]
- Calculate:
\[ p_{\text{initial}} = -6 \, \text{kg m/s} + 6 \, \text{kg m/s} = 0 \, \text{kg m/s} \]

4. **Determine the final momentum after the collision:**
- After the collision, the two bodies stick together, so their combined mass (m_total) is:
\[ m_{\text{total}} = m_1 + m_2 = 2 \, \text{kg} + 3 \, \text{kg} = 5 \, \text{kg} \]
- Let the common velocity after the collision be \( V \). The final momentum (p_final) is:
\[ p_{\text{final}} = m_{\text{total}} \cdot V = 5 \, \text{kg} \cdot V \]

5. **Apply the conservation of momentum:**
- According to the conservation of momentum:
\[ p_{\text{initial}} = p_{\text{final}} \]
- Therefore:
\[ 0 = 5 \, \text{kg} \cdot V \]

6. **Solve for the common velocity \( V \):**
- From the equation \( 0 = 5 \, \text{kg} \cdot V \), we can see that:
\[ V = 0 \, \text{m/s} \]

### Final Answer:
The common velocity after the collision is **0 m/s**.