In the given figure, a smooth parabolic wire track lies in the `xy`-plane (vertical). The shape of track is defined by the equation `y=x^(2)`. A ring of mass `m` which can slide freely on the wire track, is placed at the position `A (1,1)`. The track is rotated with constant angular speed `omega` such that there is no relative slipping between the ring and the track. The value of `omega` is

A point charge +q is fixed at point A on the circumference of a fixed smooth non-conducting circular wire track of radius R in a gravity free space. A small ring of mass m and charge + which can slide freely on the wire track is given tangential velocity at point B which is diametrically opposite to A . If the distance of closest approach between the fixed charge and the ring is R then force applied by the wire track on the ring just after the release will be

A small ring P is threaded on a smooth wire bent in the form of a circle of radius a and centre O. The wire is rotating with constant angular speed omega about a vertical diameter xy, while the ring remains at rest relative to the wire at a distance (a)/(2) from xy. Then omega^2 is equal to:

A small ring P is threaded on a smooth wire bent in the form of a circle of radius a and centre O. The wire is rotating with constant angular speed omega about a vertical diameter xy, while the ring remains at rest relative to the wire at a distance (a)/(2) from xy. Then is equal to:

A small of mass m starts from rest at the position shown and slides along the frictionless loop the loop track of radius R. What is the smallest value of y such that the object will slide without losing contact with the track?

A small of mass m starts from rest at the position shown and slides along the frictionless loop the loop track of radius R. What is the smallest value of y such that the object will slide without losing contact with the track?

A small of mass m starts from rest at the position shown and slides along the frictionless loop the loop track of radius R. What is the smallest value of y such that the object will slide without losing contact with the track?

A toy train of mass M is moving on a circular track of radius R with constant speed v. The length of the train is half of the perimeter of the track. The linear momentum of the train will be

A smooth semicircular wire-track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R//4 is attached to the lowest point O of the wire-track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held staionary at point P such that the spring makes an angle of 60^@ with the vertical. The spring constant K=mg//R . Consider the instant when the ring is released, and (i) draw the free body diagram of the ring, (ii) determine the tangential acceleration of the ring and the normal reaction.

A smooth semicircular wire-track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R//4 is attached to the lowest point O of the wire-track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held staionary at point P such that the spring makes an angle of 60^@ with the vertical. The spring constant K=mg//R . Consider the instant when the ring is released, and (i) draw the free body diagram of the ring, (ii) determine the tangential acceleration of the ring and the normal reaction.