A body moving towards a finite body at rest collides with it. It is possible that

Options

A. both the bodies come to rest
B. both the bodies move after collision
C. the moving body comes to rest and the stationary body starts moving
D. the stationary body remains stationary, the moving body changes its velocity

Answer

To solve the problem of a body moving towards a finite body at rest and colliding with it, we will analyze the situation using the principle of conservation of momentum.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the mass of the moving body be \( m_1 \) and its initial velocity be \( V \).
- Let the mass of the stationary body be \( m_2 \) and its initial velocity be \( 0 \).

2. **Write the Conservation of Momentum Equation**:
- According to the law of conservation of momentum, the total momentum before the collision must equal the total momentum after the collision.
- Before the collision, the momentum is:
\[ \text{Initial Momentum} = m_1 \cdot V + m_2 \cdot 0 = m_1 V \]
- After the collision, let the velocities of the bodies be \( V_1 \) (for \( m_1 \)) and \( V_2 \) (for \( m_2 \)). The momentum after the collision is:
\[ \text{Final Momentum} = m_1 V_1 + m_2 V_2 \]
- Setting the initial momentum equal to the final momentum gives us:
\[ m_1 V = m_1 V_1 + m_2 V_2 \]

3. **Analyze Possible Outcomes**:
- **Option A**: Both bodies come to rest. This means \( V_1 = 0 \) and \( V_2 = 0 \). The equation becomes:
\[ m_1 V = 0 + 0 \quad \text{(not possible since } m_1 V \neq 0\text{)} \]
- **Option B**: The moving body comes to rest, and the stationary body starts moving. This means \( V_1 = 0 \) and \( V_2 \) is some non-zero value. The equation becomes:
\[ m_1 V = m_2 V_2 \quad \text{(possible if } V_2 = \frac{m_1 V}{m_2}\text{)} \]
- **Option C**: The stationary body remains stationary, and the moving body changes its velocity. This means \( V_2 = 0 \) and \( V_1 \) is some non-zero value. The equation becomes:
\[ m_1 V = m_1 V_1 + 0 \quad \text{(not possible since } V_1 \neq V\text{)} \]

4. **Conclusion**:
- From the analysis, we find that:
- Option A is not possible.
- Option B is possible.
- Option C is not possible.
- Therefore, the only feasible outcome is that the moving body comes to rest while the stationary body starts moving.

### Final Answer:
- It is possible that the moving body comes to rest and the stationary body starts moving (Option B).