Various expressions for the kinetic energy

[hangainlover]

Homework Statement

Suppose that a hole is drilled through the center of Earth to the other side along its axis. A small object of mass m is dropped from rest into the hole at the surface of Earth, as shown above. If Earth is assumed to be a solid sphere of mass M and radius R and friction is assumed to be negligible, correct expressions for the kinetic energy of the mass as it passes Earth's center include which of the following?

the given choices are as follows:
a) (1/2) MgR
b) (1/2)mgR
c) (GmM)/(2R)

Homework Equations

Due to the conservation of energy, i said Potential energy = the final kinetic energy

So, on the surface of the Earth, the total potential energy = -(GmM)/R
this should equal kinetic energy

The Attempt at a Solution

I thought the answer should be (GmM)/R but none of them matches my answer.

 

[ehild]

You assumed that the potential energy is 0 in the centre of Earth. Is it true?

ehild

 

[hangainlover]

yes cause GMm/R^2 R approaches 0

 

[ehild]

If R approaches 0 your expression goes to infinity.

ehild