A mass m is placed at P a distance h along the normal through the centre O of a this circular ring of mass M and radius r (shown in the figure)

If the mass is removed further away such that OP becomes 2h, by what factor the force of gravitation will decrease, If h = r?

A cyclist starats from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in the figure.If he maintains constant speed of 10 ms^(-1) , what is his acceleration at point R in magnitude and direction?

A satellite of mass 'm' is revolving in a circular orbit of radius 'r' around the earth of mass M. What is the total energy of the satellite?

A paticle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum, then the radial force acting on the particle is

A small body of mass m slides down from the top of a frictionless hemispherical surface of radius r as shown in the figure.The vertical height h below the highest point at which the body gets separated from the hemispherical surface. .

A magnetic field vecB is confined to a region r le a and points out of the paper (the z axis), r = 0 being the centre of the circular region. A charged ring (charge = Q) of radius b, b>a and mass m lies in the x-y plane with its centre at the origin. The ring is free to rotate and is at rest. the magnetic field is brought to zero in time Deltat . Find the angular velocity omega of the ring after the field vanishes.

A block of mass m is attached to two unstrecthed of spring constant k_1 and k_2 as shown in the figure The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.

Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR^2//4 , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

A small sphere rolls down without slipping from the top of a track in a vertical plane. The track has an elevated section and a horizontal part is 1.0 m above the ground level and the top of the track is 2.4 m above the ground. Find the distance on the ground with respect to the point B (which is vertically ) below the end of the track as shown in figure. Where the sphere lands. During its flight as a projectile does the sphere continue to rotate about its centre of mass? Explain.