Choose the correct statements from the following

Options

A. The general form of Newton's second law of motion is `vecF_(ext)=vecma`
B. A body can have energy and get no momentum.
C. A body having momentum must necessarily have kinetic energy.
D. The relative velocity of two bodies in a head-on elastic collision remains unchanged in magnitude and direction.

Explanation

To solve the question of choosing the correct statements regarding Newton's laws and momentum, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Analyze Option A:**
- Statement: "The general form of Newton's second law of motion is that F external is equal to M into a."
- Explanation: This statement is correct. Newton's second law states that the net external force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). Therefore, Option A is correct.

2. **Analyze Option B:**
- Statement: "A body can have energy and no momentum."
- Explanation: This statement is also correct. For example, consider a ball held at a height \( h \). The ball has gravitational potential energy given by \( PE = mgh \). However, since the ball is not moving, its velocity \( v = 0 \), and thus its momentum \( p = mv = 0 \). Therefore, Option B is correct.

3. **Analyze Option C:**
- Statement: "A body having momentum must necessarily have kinetic energy."
- Explanation: This statement is correct as well. Momentum \( p = mv \) implies that if a body has momentum, it must have mass \( m > 0 \) and velocity \( v \neq 0 \). Since kinetic energy \( KE = \frac{1}{2} mv^2 \) depends on velocity, if the body has momentum, it must also have kinetic energy. Therefore, Option C is correct.

4. **Analyze Option D:**
- Statement: "Relative motion of two bodies in a head-on elastic collision remains unchanged in magnitude and direction."
- Explanation: This statement is incorrect. In a head-on elastic collision, while the magnitude of the relative velocity before and after the collision may remain the same, the direction of the relative velocity changes. For instance, if two bodies collide, the direction of their velocities reverses after the collision. Therefore, Option D is incorrect.

### Conclusion:
Based on the analysis:
- **Correct Options:** A, B, and C
- **Incorrect Option:** D

### Final Answer:
The correct statements are A, B, and C.

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