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Q.

A bead of mass m is attached to one end of a spring of natural length R and spring constant k=(3+1)mgR. The other end of the spring is fixed at a point A on a smooth vertical ring of radius R as shown in the figure. The normal reaction at B just after it is released to move is

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a

mg/2

b

3mg

c

33mg

d

33mg2

answer is D.

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Detailed Solution

Extension in the spring isx=AB−R=2Rcos⁡30∘−R=(3−1)R Spring force: F=kx=(3+1)mgR×(3−1)R=2mgFrom the figure we haveN=(F+mg)cos⁡30∘=33mg2
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A bead of mass m is attached to one end of a spring of natural length R and spring constant k=(3+1)mgR. The other end of the spring is fixed at a point A on a smooth vertical ring of radius R as shown in the figure. The normal reaction at B just after it is released to move is