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# Which of the following is true, if no work is done by a force on an object?

(1) the object is stationary
(2) the force is always perpendicular to its velocity
(3) the force is always perpendicular to its acceleration
(4) the object moves in such a way that the point of application of the force remains fixed

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## 1 Answer

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Answer: (1), (2) and (4)
Work done by a constant force $W= Fd \cos \theta$
(1) If the object is stationery even when the force is applied, $d = 0 \rightarrow W = 0$
(2) If the force is perpendicular to velocity $\rightarrow \theta = 90^\circ \rightarrow W = 0$, as $\cos 90 = 0$
(4) If the object moves in such a way that the point of application remains fixed then this is an example of circular motion, where the angle $\theta$ between force and displacement is $90^\circ \rightarrow W = 0$ (same math as (2))
(3) is not true as acceleration does not convet direction of displacement unlike velocity.
answered Aug 25, 2014

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