Motion Of A Ball In A Tunnel Through The Earth

Motion of earth has

Problems On Tunnel

Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point a distance h directly above the tunnel. The motion of the particle as seen from the earth is

A ball of mass m is dropped from a height h equal to the radius of the earth above the tunnel dug through the earth as shows in the figure. Choose the correct options. (Mass of earth = M )

Which of the following statements is/are correct? If we dug a tunnel through the body of the earth and put an object into it, its will undergo simple harmonic motion, oscillating in to between two extreme surfaces of the earth The value of g is zero at the centre of the earth.Choose the correct option.

Consider the earth as a uniform sphere if mass M and radius R . Imagine a straight smooth tunnel made through the earth which connects any two points on its aurface. Show that the motion of a particle of mass m along this tunnel under the action of gravitation would be simple harmonic. Hence, determine the time that a particle would take to go from one end to the other through the tunnel.

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)