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In non-uniform circular motion, the work done by force should not be zero because tangential force acts on body. Is this correct? If I am wrong, please give a proper explanation.

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Yes, this is correct. The tangential force will act as a torque on the body, increasing its angular velocity and thus also increasing its kinetic energy. By the work-kinetic-energy theorem, work has been done on the body.

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Yes, in non-uniform circular motion the work done on the object is non-zero, for the reason you stated. If the object is accelerating in the tangential direction, then that means a force (or a component of a force) is being exerted in the tangential direction. Because some component of force is being exerted in the direction of motion of the object, work is being done on the object.

However, there is still no work done by the radial components of forces, or more succinctly, by the centripetal force. For an object in circular motion, the centripetal force is perpendicular to the direction of motion of the object, and so no work is being down by the centripetal force. This is true whether the motion is uniform or not.

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Of course. . . Work done is stored in the body as its rotational kinetic energy i.e, $$\tau \theta = \Delta KE_{rot}$$ If torque is zero, then $\tau=0$ and thus there is no change in rotational kinetic energy. Then the motion is said to be uniform circular motion.

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