Which of the following statement is wrong?

Options

A. KE of a body is independent of the direction of motion
B. In an elastic collision of two bodies, the momentum and energy of each body is conserved
C. If two protons are brought towards ech other, the PE of the system increases
D. A body can have energy without momentum

Answer

To determine which statement is wrong among the given options, we will analyze each statement one by one.

### Step 1: Analyze Statement A
**Statement A:** "The kinetic energy of bodies is independent of direction of motion."

**Analysis:**
- Kinetic energy (KE) is defined as \( KE = \frac{1}{2} mv^2 \), where \( m \) is mass and \( v \) is speed.
- Speed is a scalar quantity and does not depend on direction. Thus, the kinetic energy of a body is indeed independent of the direction of its motion.

**Conclusion:** Statement A is correct.

### Step 2: Analyze Statement B
**Statement B:** "In an elastic collision of two bodies, the momentum and energy of each body is conserved."

**Analysis:**
- In an elastic collision, the total momentum of the system is conserved, but the momentum of each individual body is not necessarily conserved due to the forces acting during the collision.
- Similarly, while the total kinetic energy of the system is conserved, the kinetic energy of each individual body can change during the collision.
- Therefore, this statement is misleading because it implies that both momentum and energy are conserved for each individual body, which is not true.

**Conclusion:** Statement B is incorrect.

### Step 3: Analyze Statement C
**Statement C:** "If two protons are brought to each other, the potential energy of the system increases."

**Analysis:**
- Protons are positively charged and will repel each other due to electrostatic force.
- As they are brought closer together, work must be done against this repulsive force, which increases the potential energy of the system.
- Thus, this statement is correct.

**Conclusion:** Statement C is correct.

### Step 4: Analyze Statement D
**Statement D:** "A body can have energy without momentum."

**Analysis:**
- A body can possess kinetic energy even if its net momentum is zero. For example, consider a gas where molecules move in random directions; the total momentum can sum to zero while the kinetic energy remains positive due to the individual motions of the molecules.
- Therefore, this statement is also correct.

**Conclusion:** Statement D is correct.

### Final Conclusion
After analyzing all statements, we find that:

- **Statement A:** Correct
- **Statement B:** Incorrect (this is the wrong statement)
- **Statement C:** Correct
- **Statement D:** Correct

Thus, the wrong statement is **Statement B**.

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