A tunnel is dug across the earth of mass 'M' and radius 'R' at a distance `R//2` from the centre 'O' of the Earth as shown. A body is released from rest from one end of the smooth tunnel. The velocity acquired by the body when it reaches the centre 'C' of the tunnel is

A tunnel is dug along a chord of the earth at a perpendicular distance R//2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall, and the acceleration of the particle vary with x (distance of the particle from the centre) according to

A tunnel has been dug through the centre of the earth and a ball is released in it. It will reach the other end of the tunnel after

A body starts from rest from a point distant r_(0) from the centre of the earth. It reaches the surface of the earth whose radius is R . The velocity acquired by the body is

A tunnel is dug through the centre of the earth. Shwo that a body of mass m when dropped form rest from one end of the tunnel will execute simple harmonic motion.

A tunnel ois dug along a chord of the earth a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. Find the force exerted by the eall on a particle of mass m when it is at a distance x from the centre of the tunnel.

A tunnel is dug along a chord of non rotating earth at a distance d=(R)/(2) [R = radius of the earth] from its centre. A small block is released in the tunnel from the surface of the arth. The block comes to rest at the centre (C) of the tunnel. Assume that the friction coefficient between the block and the tunnel wall remains constant at mu. Calculate work done by the friction on the block. Calculate mu.

The weight of a body a distance 2R from the centre of the earth of radius 'R' is 2.5 N. If the distance is 3R from the centre of the earth the weight of the body will be

(a) A tunnel is dug along a diameter of the earth. Find the force on the a particle of mass m placed in the tunnel at a distance x from the centre. (b) A tunnel is dug along a chord of the earth at a perpendicular distance R//2 from the earth's centre. the wall of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.