`AB` is a light rigid rod. Which is rotating about a vertical axis passing through `A,A` spring of force constant `K` and natural length `l` is attached at `A` and its other end is attached to a small bead of mass `m`. The bead can slide without friction on the rod. At the initial moment the bead is at rest (w.rt. the rod) and the spring is unstreached Select correct option

A ring of mass m is attached to a horizontal spring of spring constant k and natural length l_0 . The other end of the spring is fixed and the ring can slide on a horizontal rod as shown. Now the ring is shifted to position B and released Find the speed of the ring when the spring attains its natural length.

A bead of mass m can slide without friction along a vertical ring of radius R. One end of a spring of force constant k=(3mg)/(R ) is connected to the bead and the other end is fixed at the centre of the ring. Initially, the bead is at the point A and due to a small push it starts sliding down the ring. If the bead momentarily loses contact with the ring at the instant when the spring makes an angle 60^(@) with the vertical, then the natural length of the spring is

A bead of mass m can slide without friction along a vertical ring of radius R. One end of a spring of force constant k=(3mg)/(R ) is connected to the bead and the other end is fixed at the centre of the ring. Initially, the bead is at the point A and due to a small push it starts sliding down the ring. If the bead momentarily loses contact with the ring at the instant when the spring makes an angle 60^(@) with the vertical, then the natural length of the spring is

One end of a light spring of natural length d and spring constant k is fixed on a rigid wall and the other is attached to a smooth ring of mass m which can slide without friction on a vertical rod fixed at a distance d from the wall. Initially the spring makes an angle of 37^(@) with the horizontal as shown in fig. When the system is released from rest, find the speed of the ring when the spring becomes horizontal. [ sin 37^(@) = 3/5]

One end of a light spring of natural length d and spring constant k is fixed on a rigid wall and the other is attached to a smooth ring of mass m which can slide without friction on a vertical rod fixed at a distance d from the wall. Initially the spring makes an angle of 37^(@) with the horizontal as shown in fig. When the system is released from rest, find the speed of the ring when the spring becomes horizontal. [ sin 37^(@) = 3/5]

On end of a light spring of natural length d and spring constant k is fixed on a rigid wall and the other is attached to a smooth ring of mass m which can slide without friction on a vertical rod fixed at a distance d from the wall. Initially the spring makes an angle of 37^@ with the horizontal. as shown in figure. When the system is released from rest, find the speed of the ring when the spring becomes horizontal. (sin 37^@=3/5) .