Question
Class 11PhysicsWork, Energy and Power
Show that moment of a couple does not depend on the point about which you take the moments.
Verified Answer
Consider a couple as shown in the figure acting on a rigid body.
The forces F and −F act respectively at points B and A. These points have position vectors r1 and r2 with respect to the origin O. Let us take the moments of the forces about the origin.
The moment of the couple = sum of the moments of the two forces making the couple
= r1 × (−F) + r2 × F = r2 × F − r1 × F = (r2 − r1) × F
r1 + AB = r2 and hence AB = r2 − r1.
AB × F . But r1 + AB = r2 and hence AB = r2 − r1.
The moment of the couple, therefore, is AB × F; which is independent of the origin, the point about which moments of the forces is taken.