A body moving with a certain speed collide with another body of finite mass kept at rest . Which of the following is/are possible ?

Options

A. Both bodies move after collision .
B. Both the bodies come to rest after collision .
C. Moving body comes to rest and body at rest starts moving .
D. Body at rest remains at rest whereas moving body rebounds and reverses its direction of motion .

Explanation

To solve the problem, we need to analyze the possible outcomes of a collision between a moving body and a stationary body while considering the law of conservation of linear momentum.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have two bodies: Body 1 (mass \( m_1 \)) moving with initial velocity \( u_1 \) and Body 2 (mass \( m_2 \)) at rest (initial velocity \( u_2 = 0 \)).
- We need to analyze the possible outcomes after the collision.

2. **Applying Conservation of Momentum**:
- The law of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision.
- Mathematically, this can be expressed as:
\[ m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \]
- Since \( u_2 = 0 \), the equation simplifies to:
\[ m_1 u_1 = m_1 v_1 + m_2 v_2 \]

3. **Analyzing Each Option**:
- **Option A**: Both bodies move after the collision.
- This is possible. Both bodies can have non-zero velocities \( v_1 \) and \( v_2 \) after the collision, satisfying the momentum equation.

- **Option B**: Both bodies come to rest after the collision.
- This is not possible. If both bodies come to rest, then \( v_1 = 0 \) and \( v_2 = 0 \), leading to \( m_1 u_1 = 0 \), which contradicts the initial condition that \( m_1 \) is moving.

- **Option C**: The moving body comes to rest and the body at rest starts moving.
- This is possible. If \( v_1 = 0 \) and \( v_2 \) is some finite value, we can rearrange the momentum equation to find \( v_2 \):
\[ m_1 u_1 = m_2 v_2 \implies v_2 = \frac{m_1}{m_2} u_1 \]
- This satisfies the conservation of momentum.

- **Option D**: The body at rest remains at rest while the moving body rebounds.
- This is not possible. If the body at rest remains at rest, then \( v_2 = 0 \). The equation becomes \( m_1 u_1 = m_1 v_1 \), which implies \( v_1 = u_1 \). This means the moving body does not change direction, contradicting the condition that it rebounds.

4. **Conclusion**:
- The possible outcomes after the collision are:
- **Option A**: Both bodies move after collision.
- **Option C**: The moving body comes to rest, and the body at rest starts moving.
- Therefore, the correct answers are **Option A** and **Option C**.