A massless rope is wrapped around a ring (with a groove along its circumference) having radius `R` and mass `m`. The ring is allowed to move download. The linear acceleration of the ring is

An impulse J is applied on a ring of mass m along a line passing through its centre O . The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is

An impulse J is applied on a ring of mass m along a line passing through its centre O . The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is

Find the centre of mass of a uniform semicircular ring of radius R and mass M .

Find the centre of mass of a uniform semicircular ring of radius R and mass M .

A uniform semicurcular ring having mass m and radius r is hanging at one of its ends freely as shown if Fig. The ring is slightly disturbed so the it oscillates in its own plane. The time period of oscillation of the ring is

A uniform rope tightly wraps around a uniform thin ring the mass M and radius R. The mass of the segment of the rope around the ring (i.e. , mass of the length 2 pi R of the rope) is also M. The ends of the rope are fixed one above the other and it is taut. The ring is let go. Find its acceleration. Assume no slipping and thickness of the rope to be negligible.

A metal ring is held horizontally with the ground and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is