Work done by a force on an object is zero, if

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the force is always perpendicular to its acceleration

the force is always perpendicular to its velocity

the object is stationary but the point of application of the force moves on the object

the object moves in such a way that the point of application of the force remains fixed.

answer is B, C, D.

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Detailed Solution

Work done by a force on an object may not be zero if net acceleration is perpendicular to the force, hence (A) is not correct.

If displacement of the object is zero, then work done is zero, even if the point of application of the force is moving on it (Example, work done by friction on a block sliding on the floor is not zero, but work done by same friction on the floor is zero). Hence (B) is correct.

When a force is always perpendicular to velocity, work done is zero as 𝑊 = ∫𝐹 . 𝑑𝑠̅ = 0, as instantaneous displacement is always perpendicular to the force. (Example, work done by centripetal force on an object moving in circular path is zero). Hence (C) is correct.

In pure rolling motion, work done by friction is zero. Though the body is moving, the point of application of friction is always at instantaneous rest. Hence (D) is correct.

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