Question

The moment of a couple is given by

• A. Force \(\times\) Area
• B. Force \(\times\) Time
• C. Force \(\times\) Inertia
• D. Force \(\times\) Perpendicular distance

Hint:

Moment of a couple equals one force multiplied by the perpendicular distance between the two forces.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A "couple" in mechanics is a pair of forces that are equal in magnitude, opposite in direction, and act on parallel lines. A couple produces a pure turning effect, or moment, without any net translation. The question asks for the formula to calculate this turning effect, i.e., the moment of the couple.
Step 2: Key Formula or Approach:
The moment of a couple (M) is defined as the product of the magnitude of one of the forces (F) and the perpendicular distance (d) between the lines of action of the two forces. \[ M = F \times d \] Step 3: Detailed Explanation:
1. Consider two parallel forces, F and -F, separated by a perpendicular distance d. 2. These two forces form a couple. 3. The net force of the couple is F + (-F) = 0, so the couple does not cause any linear acceleration. 4. However, the couple does produce a turning effect (a moment or torque). The magnitude of this moment is calculated by taking the moment of the two forces about any point. 5. If we take moments about a point on the line of action of one force, the moment due to that force is zero. The moment due to the other force is its magnitude (F) multiplied by the lever arm, which is the perpendicular distance (d). 6. So, the total moment is $M = F \times d$. This moment is the same regardless of the point about which it is calculated. 7. Let's look at the options. Option (D) Force $\times$ Perpendicular distance is the correct definition of the moment of a couple. 8. The other options represent different physical quantities: Force $\times$ Time is Impulse; Force $\times$ Area is related to pressure concepts; Force $\times$ Inertia is not a standard physical quantity. Step 4: Final Answer:
The moment of a couple is given by the product of the magnitude of one of the forces and the perpendicular distance between them. Therefore, option (D) is the correct answer.