A bead of mass 5 kg is free to slide on the horizontal rod AB. They are connected to two identical springs of natural length h ms. As shown. If initially bead was at O & M is vertically below L then, velocity of bead at point N will be :

A bead C can move freely on a horizontal rod. The bead is connected by blocks B and D by a string as shown in the figure. IF the velocity of B is v. find the velocity of block D.

A bead B of mass 'm' can travel without frictionn on a smooth horizontalwire "xx"^(') . The bead is connected to a block of identical mass by an ideal string passing over an ideal pulley. The system, as shown, is in vertical plane. System is initially released from rest in the position shown. Initial acceleration of block A is:

In the shown figure two beads slide along a smooth horizontal rod as shown in figure. The relation between v and v_(0) in the shown position will be

Beads A and B each of mass m , are connected by a light inextensible cord. They are constrained (restricted) to move on a frictionless ring in a vertical plane as shown. The beads are released from rest at the position shown. The tension in the cord just after the release 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

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 on a fixed circular horizontal ring of radius 3R having a centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A, then the kinetic energy of the bead when it reaches point B is

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3R having a centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A, then the kinetic energy of the bead when it reaches point B is