A body moving towards a body of finite mass collides with it. It is possible that

Options

A. both bodies come to rest
B. both bodies move after collision
C. the moving body stops and the body moving must have same mass
D. the stationary body remains stationary and the moving body rebounds

Explanation

To solve the problem, we need to analyze the possible outcomes of a collision between a moving body and a stationary body of finite mass. Let's denote the moving body as \( m \) and the stationary body as \( M \).

### Step-by-Step Solution:

1. **Understanding the Collision**:
- When a body \( m \) moves towards a stationary body \( M \) and collides with it, the nature of the collision (elastic or inelastic) will determine the outcomes.

2. **Coefficient of Restitution**:
- The coefficient of restitution \( e \) can take values between 0 and 1, where:
- \( e = 0 \): Perfectly inelastic collision (bodies stick together).
- \( e = 1 \): Perfectly elastic collision (kinetic energy is conserved).

3. **Analyzing Option A**:
- **"A body will come to rest"**:
- This is not possible because if body \( m \) collides with \( M \), it cannot come to rest unless it has the same mass and velocity, which is a special case. In general, body \( m \) will either stick to \( M \) or transfer some of its momentum to \( M \).
- **Conclusion**: Option A is incorrect.

4. **Analyzing Option B**:
- **"Both bodies move after the collision"**:
- This is possible in the case of a perfectly inelastic collision (where they stick together) or in an elastic collision where both bodies move after the impact.
- **Conclusion**: Option B is correct.

5. **Analyzing Option C**:
- **"The moving body stops and the body must have the same mass"**:
- This can happen in a perfectly elastic collision where both bodies have the same mass. In this case, the moving body \( m \) can transfer all its momentum to \( M \) and come to rest.
- **Conclusion**: Option C is correct under the condition that both bodies have the same mass.

6. **Analyzing Option D**:
- **"The stationary body remains stationary and the moving body rebounds"**:
- This is not possible because if \( M \) is of finite mass, it cannot remain stationary when a moving body collides with it. The finite mass \( M \) will always respond to the collision.
- **Conclusion**: Option D is incorrect.

### Final Answer:
- The correct options are **B and C**.