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Angular momentum of a particle rotating under a central force is constant due to

Asked in AIEEE 2007 · Conservation of angular momentum

(1) constant torque
(2) constant force
(3) constant linear momentum
(4) zero torque

Answer: (4) zero torque

Step-by-step solution

A central force acts along ⃗r, so its torque about the centre is τ⃗=⃗r×⃗F=0.

With zero torque, (d⃗L)/(dt)=0, so angular momentum is conserved.

Why the other options are wrong

(1) A constant non-zero torque would change L, not keep it constant.
(2) A central force is generally not constant in magnitude or direction.
(3) Linear momentum is not conserved for circular or elliptical central-force motion.

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