A bead of mass m slides without friction on the wall of a vertical circular hoop of radius R as shown in figur…

Question

A bead of mass $$m$$ slides without friction on the wall of a vertical circular hoop of radius $$R$$ as shown in figure. The bead moves under the combined action of gravity and a massless spring $$k$$ attached to the bottom of the hoop. The equilibrium length of the spring is $$R$$. If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes $$R$$, would be (spring constant is $$k$$, $$g$$ is acceleration due to gravity):

Accepted Answer

A. $$\sqrt{3Rg + \frac{kR^2}{m}}$$

Answer

B. $$\sqrt{2Rg + \frac{kR^2}{m}}$$

Answer

C. $$2\sqrt{gR + \frac{kR^2}{m}}$$

Answer

D. $$\sqrt{2Rg + \frac{4kR^2}{m}}$$

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