Bill, a slightly wacky engineer, proposes to build a tunnel all the way through

Question

Bill, a slightly wacky engineer, proposes to build a tunnel all the way through the center of the earth and out the other side. Although they tell Bill that it's impossible, it sounds too exciting an idea to give up. If the tunnel were to be evacuated so that there was almost no friction, what would the kinetic energy be of an object of mass 87kg at the center of the Earth assuming that is was dropped from rest at the surface? Ta the radius of the earth to be about 6.37 x 100m and the acceleration of gravity at the earth's surface to be 9.81 Assume that the density of the earth is uniform. Submit

Explanation / Answer

The kinetic energy of the mass will be equal to mgR = 87x9.81x6.37x106 = 5436603900 J

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