Question

Show the moment of a couple does not depend on the point about which take the moment.

Answer 1

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Let us consider the given figure in attachment.Here two fores are acting on a body at point A and B.

The position vectors are r1 and r2.

Moment of the couple =r1x F +r2(-F)=r1-r2x F------ equation (1)

in Triangle OAB
r2+BA=r1

BA=r1-r2 ----- (equation 2)
From equation 1 and 2

Moment of Couple = BA x F
from the above equation it is evident that moment of couple is independent of the origin.

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