
A particle of mass is free to slide on a smooth ring of radius fixed in a vertical plane. The particle attached to one end of a spring whose other end is fixed to the top point of the ring. Initially the particle is at rest at a point of the ring such that being the centre of the ring. The natural length of the spring is also equal to . After the particle is released and slides down the ring the contact force between the particle and the ring becomes zero when it reaches the lowest position (diametrically opposite to ). Determine the force constant of the spring.


Important Questions on Work, Power, and Energy



A weightless rod of length carries two equal masses , one tied at the lower end and the other at the middle of the rod at . The rod can rotate in a vertical plane about a fixed horizontal axis passing through . The rod is released from rest in a horizontal position. The speed of the mass at the instant rod become vertical is

A particle is rotated in a vertical circle by connecting it to a light rod of length and keeping the other end of the rod fixed. The minimum speed of the particle when the light rod is horizontal for which the particle will complete the vertical circle is,


A small block slides with velocity on the horizontal frictionless surface as shown in the figure. The block leaves the surface at the point . The angle in the figure is

A particle moves from rest at on the surface of a smooth circular cylinder of radius as shown. At , it leaves the cylinder. The equation relating and is
