Which of the following statement is correct?

Options

A. Kinetic energy of a system can be changed without changing its momentum
B. Kinetic energy of a system cannot to be changed without changing its momentum
C. Momentum of a system cannot be changed without changing its kinetic energy
D. Body cannot have energy without having momentum.

Answer

To determine which statement is correct regarding kinetic energy and momentum, we can analyze each option step by step:

### Step 1: Understand the Definitions
- **Kinetic Energy (KE)**: The energy that an object possesses due to its motion, given by the formula \( KE = \frac{1}{2} mv^2 \), where \( m \) is mass and \( v \) is velocity.
- **Momentum (p)**: The quantity of motion of a moving body, calculated as \( p = mv \).

### Step 2: Analyze Statement A
- **Statement A**: "The kinetic energy of the system can be changed without changing its momentum."
- **Analysis**: Consider a scenario where two bodies collide. During the collision, kinetic energy may be converted into potential energy (e.g., elastic potential energy during deformation). However, the total momentum of the system remains constant (conserved). Thus, it is possible for kinetic energy to change while momentum remains unchanged.
- **Conclusion**: Statement A is **correct**.

### Step 3: Analyze Statement B
- **Statement B**: "The kinetic energy of the system can't be changed without changing its momentum."
- **Analysis**: This contradicts Statement A. Since we established that kinetic energy can change while momentum remains constant during collisions, this statement is false.
- **Conclusion**: Statement B is **incorrect**.

### Step 4: Analyze Statement C
- **Statement C**: "The momentum of the system can't be changed without changing its kinetic energy."
- **Analysis**: Momentum can change independently of kinetic energy. For instance, if a body changes direction while maintaining the same speed, its momentum changes but its kinetic energy remains the same.
- **Conclusion**: Statement C is **incorrect**.

### Step 5: Analyze Statement D
- **Statement D**: "A body can't have energy without having momentum."
- **Analysis**: A body can have potential energy (e.g., gravitational potential energy) without having momentum. For example, an object at rest at a height has potential energy but zero momentum.
- **Conclusion**: Statement D is **incorrect**.

### Final Conclusion
The only correct statement is **Statement A**: "The kinetic energy of the system can be changed without changing its momentum."

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