A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3 R having a centre at the point C . The bead is attached to one of the ends of spring with spring constant k . The natural length of spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A , then the kinetic energy of the bead when it reaches point B is

Question

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3 R having a centre at the point C . The bead is attached to one of the ends of spring with spring constant k . The natural length of spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A , then the kinetic energy of the bead when it reaches point B is, 25 2 k R 2, 9 2 k R 2, 8 k R 2, 12 k R 2

MARKS App · Accepted Answer

Given, Mass of bead = m The radius of circular horizontal ring = 3 R The natural length of spring = R According to the conservation of energy, KE i + PE i = KE f + PE f ⇒ 0 + 1 2 k OA - R 2 = KE f + 1 2 k OB - R 2 ⇒ 0 + 1 2 k 5 R - R 2 = KE f + 1 2 k R - R 2 ⇒ KE f = 8 k R 2

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