Q.A couple produces,

Step 1. Recall what defines a couple.

A couple consists of two forces $\vec F$ and $-\vec F$ — equal in magnitude, opposite in direction — whose lines of action are separated by a nonzero perpendicular distance $d$ (they do not act along the same line).

Step 2. Compute the net force.

Since Newton's second law for the center of mass gives $\vec F_{net} = M\vec a_{CM}$, a zero net force means $\vec a_{CM}=0$: the center of mass does not accelerate, so there is no translational motion produced by a couple.

Step 3. Compute the net torque.

Even though the forces cancel, they act along different lines, separated by $d$. Taking torques about any point, the two torques add rather than cancel (because both forces try to turn the body the same rotational way about the gap between them), giving a nonzero net torque

This nonzero torque produces angular acceleration, $\alpha = \tau_{net}/I \neq 0$.

Step 4. Combine the two results.

Zero net force + nonzero net torque = no translation, but definite rotation. That is exactly pure rotation, with the body spinning about its own center of mass while that center of mass stays put (e.g., turning a steering wheel or a screwdriver knob with two fingers).

Step 5. Rule out the other options.

• (b) pure translation is wrong — that would need a nonzero net force with zero net torque, the opposite of a couple.
• (c) rotation and translation is wrong — translation requires $\vec a_{CM}\neq 0$, which needs nonzero net force; a couple's net force is always zero.
• (d) no motion is wrong — the net torque is nonzero, so the body definitely does start rotating (unless already prevented by an external constraint, which isn't implied here).

• Assuming that because the forces 'cancel', the body doesn't move at all — they cancel only as forces (translation), not as torques (rotation).
• Forgetting that torque still exists even about a point where the two forces individually have zero moment arm on one side — a couple's torque is the same about every point, precisely because the forces sum to zero.