A tunnel is drilled from the surface of the earth(mass assumed to be M and radius to be R) to its center . A body of mass m is dropped from the surface to the center through the tunnel. What will be the velocity with which the body of mass m will hit the tunnel.
Loss in PE = Gain In KE
Loss in PE = PE at surface - PE at center of earth.
= |-GMm/R - 0|
1/2 mv = |-GMm/R|
v = √(2GM/R)
The Attempt at a Solution
But in a textbook , the PE at the center of earth is given to be -(3/2) (GMm/R)
what is the right way of approaching the problem.