# A small hook of mass m passes through a smooth wire bent in the form of horizontal circle (fixed) of radius R.

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A small hook of mass m passes through a smooth wire bent in the form of horizontal circle (fixed) of radius R. The hook is connected to a spring whose other end is fixed at point A on the circular wire as shown in diagram. The natural length of the spring is R and spring constant is mg/R.  Initially the hook is slightly displaced from rest from position B which is diametrically opposite to point A. The hook moves along the circular arc from position B to C. [N = normal reaction between circular wire and hook and V = speed of hook]

 List-I List-II (P) N = mg (1) At position B (Q) N = zero (2) At position C (R) Total acceleration is zero (3) Some where between B and C (S) V = √g/R (4) Never between B and C

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Correct option (A) 3 4 1 2

Explanation:

N (horizontal) changes direction from B to C, at B N (horizontal) on the hook is directed radially outward and at C directed radially inward, hence it becomes zero some where between B and C. N vertical is equal to mg therefore some where in between B & C net normal reaction is mg. At point B, ac = 0 because velocity is zero & at = 0, since no force in tangential direction.