Which of the following statements is incorrect?

Options

A. A pair of equal and opposite forces with different lines of action is known as couple.
B. A couple produces rotation without translation.
C. When we open the lid of a bottle by turning it, our fingers apply a couple to the lid.
D. Moment of a couple depends on the point about which we take the moment.

Answer

To determine which statement is incorrect regarding the concept of couples in physics, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1: A pair of equal and opposite forces with different lines of action is known as a couple.**
- A couple consists of two equal and opposite forces that do not act along the same line. This creates a rotational effect without any translational motion.
- **Conclusion:** This statement is **correct**.

2. **Statement 2: A couple produces rotation without translation.**
- By definition, a couple generates a torque that causes rotation around an axis, while the center of mass does not translate.
- **Conclusion:** This statement is **correct**.

3. **Statement 3: When we open the lid of a bottle by turning it, our fingers apply a couple to the lid.**
- When you twist the lid, your fingers exert forces in opposite directions, creating a couple that results in the rotation of the lid.
- **Conclusion:** This statement is **correct**.

4. **Statement 4: The moment of a couple depends on the point about which we take the moment.**
- The moment (torque) of a couple is defined as the product of one of the forces and the distance between the lines of action of the forces. Importantly, the moment of a couple is independent of the point about which it is calculated; it remains constant regardless of the point of reference.
- **Conclusion:** This statement is **incorrect**.

### Final Answer:
The incorrect statement is **Statement 4**: "The moment of a couple depends on the point about which we take the moment."

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