A small bead of mass $m$ can slide on a frictionless fixed ring of radius $r$ . With the help of two identical strings of force constant $k$ , the bead is connected to two nails A and B each on a diameter at a distance $0.5 r$ from centre O of the ring. Relaxed length of each string is negligible as compared to the radius of the ring. The bead is given a small velocity at point C. What can you predict about subsequent motion of the bead before any of the string strikes a nail?

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Total elastic potential energy stored in both the strings is $1.25 k r^{2}$ .

It will oscillate simple harmonically about the point C.

It will keep moving with its initial speed.

Its angular momentum about centre O of the ring is conserved.

answer is A, C, D.

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