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Asked in CBSE AIPMT 1997 · Torque and moment of a force
Idea: a couple is a pair of equal, opposite, non-collinear forces, so treat force and torque separately.
Net force: ⃗F+(-⃗F)=0, so ⃗a_cm=0 and the centre of mass does not accelerate.
Net torque about any point: τ=F× (perpendicular separation of the two lines of action), which is not zero.
Zero net force with non-zero net torque gives angular acceleration and no linear acceleration.
So a couple produces purely rotational motion.
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