A smooth circular track of mass M is vertically hung by a string down the ceiling. Two small rings, each of mass `m`, are initially at rest at the top of the track. They then slide down simultaneously along the track in opposite directions. Find the position of the rings when the tension in the string is zero.

A loop of mass M with two identical rings of mass m at its top hangs from a ceiling by an inextensible string. If the rings gently pushed horizontally in opposite directions, find the angular distance covered by each ring when the tension in the string vanishes for once during their motion.

A loop of mass M with two identical rings of mass 3/2 M each at its top hangs from a ceiling by an inextensible string. If the rings gently pushed horizontally in opposite directions, find the angular distance covered by each ring when the tension in the string vanishes for once during their motion.

A smooth semicircular wire-track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R//4 is attached to the lowest point O of the wire-track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held staionary at point P such that the spring makes an angle of 60^@ with the vertical. The spring constant K=mg//R . Consider the instant when the ring is released, and (i) draw the free body diagram of the ring, (ii) determine the tangential acceleration of the ring and the normal reaction.

A smooth semicircular wire-track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R//4 is attached to the lowest point O of the wire-track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held staionary at point P such that the spring makes an angle of 60^@ with the vertical. The spring constant K=mg//R . Consider the instant when the ring is released, and (i) draw the free body diagram of the ring, (ii) determine the tangential acceleration of the ring and the normal reaction.

A smooth semicircular wire track of radius R if fixed in a vertical plane. One end of massless spring of netural length (3R)/(4) is attached to the lowest point O of the wire track. A small ring of mass m which can slide on the track is attched to the other end of the spring. the ring is held stationary at point P such that the spring makes an angle of 60^(@) with the vertical. The spring constant is K = (mg)/(R ) . considering the instance when the ring is released, the free body diagram of the ring, when a_(T) is tengential acceleration, F is restoring force and N is normal reaction is

Two balls of mass m and 2m are attached with strings of length 2L and L respectively. They are released from horizontal position. Find ratio of tensions in the string when the acceleration of both is only in vertical direction :

A smooth track, fixed to the ground, is in the shape of a quarter of a circle. Two small blocks of mass 3m and 2m are released from the two edges A and B of the circular track. The masses slide down and collide at centre O of the track. Vertical height of A and B from O is h = 2m . Collision is elastic. Find the maximum height (above O) attained by the block of mass 2m after collision