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A uniform rod 0A of length l, resting on smooth surface is slightly disturbed from its vertical position. P is a point on the rod whose locus is a circle during the subsequent motion of the rod. Then the distance OP is equal to.. ? (in terms of "l")

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the only thing we can say is that OP is the radius of the circle it makes and that OP= L-AP
no it is solvable..

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Other answers:

i tried doin with the circle equation and taking the rod as y axis..
i dont understand what can we assume about the motion from the phrase "slightly disturbed"
the question is correct and solvable.. slightly disturbed may refer change in equilibrium position.

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