A bead of mass m is located on a parabolic wire with its axis vertical and vertex at the origin as shown in figure and whose equastion is `x^(2) =4ay`. The wire frame is fixed and the bead is released from the point `y=4a` on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by `y=a` is

A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downwards as in figure and whose equation is x^2=ay . If the coefficient of friction is mu , the highest distance above the x-axis at which the particle will be in equilibrium is

A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downwards as in figure and whose equation is x^2=ay . If the coefficient of friction is mu , the highest distance above the x-axis at which the particle will be in equilibrium is

A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downwards as in figure and whose equation is x^2=ay . If the coefficient of friction is mu , the highest distance above the x-axis at which the particle will be in equilibrium is

A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downwards as in figure and whose equation is x^2=ay . If the coefficient of friction is mu , the highest distance above the x-axis at which the particle will be in equilibrium 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

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 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