If a hole were bored through the center of a planet with uniform density, the fo

Question

If a hole were bored through the center of a planet with uniform density, the force on a mass m dropped into such a hole would be given by |F| = mgr/R , where

* r = the variable distance of of the mass from the center of the planet.

* R = the constant radius of the planet.

* g = the gravitational field strength at the surface of the planet.

If the mass were dropped from rest at the surface, what would be the speed of the mass m as it passed through the center of the planet?

How did you come to your conclusion?

[ Thanks for your help ]

Explanation / Answer

At the surface, r = R; andgravity forceon mass is: F = mg.

When mass is falling through hole, r < R; and so F = mgr/R.

At center of earth, r = 0, and so F = 0, so that a = 0.

Thus, the speed of the mass, v, is constant and maximum,

By conservation of energy: mgR =

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