A body of mass m moving with velocity `3km//h` collides with a body of mass 2m at rest. Now, the combined mass starts to move with a velocity

Options

A. `1km//h`
B. `2km//h`
C. `3km//h`
D. `4km//h`

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:**
- Mass of the first body (m1) = m
- Velocity of the first body (v1) = 3 km/h
- Mass of the second body (m2) = 2m
- Velocity of the second body (v2) = 0 km/h (since it is at rest)

2. **Write the conservation of momentum equation:**
According to the law of conservation of momentum:
\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) v \]
Substituting the known values:
\[ m \cdot 3 + 2m \cdot 0 = (m + 2m) v \]

3. **Simplify the equation:**
The left side becomes:
\[ 3m + 0 = 3m \cdot v \]
So, we have:
\[ 3m = 3m \cdot v \]

4. **Solve for the final velocity (v):**
To isolate v, divide both sides by 3m (assuming m ≠ 0):
\[ v = \frac{3m}{3m} = 1 \text{ km/h} \]

5. **Conclusion:**
The final velocity of the combined mass after the collision is:
\[ v = 1 \text{ km/h} \]

### Final Answer:
The combined mass starts to move with a velocity of **1 km/h**.

---