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

Work done by gravity 

Work done by spring 

Net work
change in kinetic energy
i.e.
or
or 
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