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## Homework Statement

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.

## Homework Equations

Loss in PE = Gain In KE

Loss in PE = PE at surface - PE at center of earth.

= |-GMm/R - 0|

1/2 mv[2] = |-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.