A bead can slide on a smooth circular wire frame of radius r which is fixed in a vertical plane. The bead is displaced slighty from the highest point of the wire frame. The speed of the bead subsequently as a function of the angle `theta` made by the bead with the verticle line is

A bead can slide on a smooth circular wire frame of radius R which is fixed in a vartical plane. The bead is displaced slightly from the highest point of the wire frame. The speed of the bead subsequently as a function of the angle theta made by the bead with the vertical line is

A bead is free to slide down a smooth wire tightly stretched between points A and B on a vertical circle. If the starts from rest at A , the heighest point on the circle

A bead of mass m is threaded on a smooth circular wire centre O , radius a, which is fixed in vertical plane. A light string of natural olength 'a', elastic constant = (3mg)/(a) and breaking strength 3mg connects the bead to the lowest point A of the wire. The other end of the string is fixed to ring at point B near point A . The string is slaked initially. The bead is projected from A with speed u . If v =2 u_(0) , the tension T in th elastic string when the bead is at the highest point B of the wire is

A bead of mass m is threaded on a smooth circular wire centre O , radius a, which is fixed in vertical plane. A light string of natural olength 'a', elastic constant = (3mg)/(a) and breaking strength 3mg connects the bead to the lowest point A of the wire. The other end of the string is fixed to ring at point B near point A . The string is slaked initially. The bead is projected from A with speed u . The elastic energy stored in the string when the bead is at the highest point B will be

A bead of mass m is threaded on a smooth circular wire centre O , radius a, which is fixed in vertical plane. A light string of natural olength 'a', elastic constant = (3mg)/(a) and breaking strength 3mg connects the bead to the lowest point A of the wire. The other end of the string is fixed to ring at point B near point A . The string is slaked initially. The bead is projected from A with speed u . The smallest value u_(0) of u for which the bead will make complete revolutions of the wire will be

Two beads of masses m_(1) and m_(2) are closed threaded on a smooth circular loop of wire of radius R. Intially both the beads are in position A and B in vertical plane . Now , the bead A is pushed slightly so that it slide on the wire and collides with B . if B rises to the height of the centre , the centre of the loop O on the wire and becomes stationary after the collision , prove m_(1) : m_(2) = 1 : sqrt(2)

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

A circular wire frame of radius R is rotating about its fixed vertical diameter. A bead on the wire remains at rest relative to the wire at a position in which the radius makes an angle theta with the vertical (see figure). There is no friction between the bead and the wire frame. Prove that the bead will perform SHM (in the reference frame of the wire) if it is displaced a little from its equilibrium position. Calculate the time period of oscillation.