MOTION OF A BALL IN A TUNNEL THROUGH THE EARTH

Assume that there is a tunnel in the shape of a circular arc through the earth. Wall of the tunnel is smooth. A ball of mass m is projected into the tunnel at A with speed v. The all comes out of the tunnel at B and escapes out of the gravity of the earth. Mass and radius of the earth are M and R respectively and radius of the circle shaped tunnel is also . Find minimum possible value of v (call it v_(0) ) If the ball is projected into the tunnel with speed v_(0) , calculate the normal force applied by the tunnel wall on the ball when it is closest to the centre of the earth. It is given that the closest distance between the ball and the centre of the earth is (R)/(2)

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R//2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :

Energy || Spring with Two Blocks Long Pendulum||Tunnel in Earth SHM

A tunnel is made across the earth passing through its center. A ball is dropped from a height h in the tunnel. The motion will be periodic with time period::

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 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