A ring of radius R is placed such that it lies in a vertical plane. The ring is fixed. A bead of mass m is constrained to move along the ring without any friction. One end of the spring is connected with the mass m and other end is rigidly fixed with the topmost point of the ring. Initially the spring is in un-extended position and the bead is at a vertical distance R from the lowermost point of the ring. The bead is now released from rest.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
K = 
at initial instant a t = g, a c = 0
at bottommost position a t = 0 a c = 0
Sol. Applying conservation of energy between initial and final position is
Loss in gravitational P.E. of the bead of mass m = gain in spring P. E.
mg R = 
K (2R – 
R) 2
Or K = 
At t = 0
a t = g
a c = 0
at lowest point
a t = 0
a c = 0
The centripetal acceleration of bead at the initial and final position is zero because its speed at both
position is zero.
The tangential acceleration of the bead at initial position is g.
The tangential acceleration of the bead at lower most position is zero.
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