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Assuming the radius of the earth as R, the change in gravitational potential energy of a body of mass m, when it is taken from the earth's surface to a height 3R above its surface, is

1. 3 mg R
2. 3/4 mg R
3. 1 mg R
4. 3/2 mg R

Correct answer: 3/4 mg R

Solution

The change in gravitational potential energy is given by ΔU = -GMm(1/r2 - 1/r1). At the surface, r1 = R, and at height 3R, r2 = 4R. Substituting and simplifying, ΔU = -GMm(1/4R - 1/R) = 3GMm/4R. Using g = GM/R^2, ΔU = 3/4 mgR.

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