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

Question

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

Infinity Learn · Accepted Answer

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

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