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Potential energy at the surface of the earth is U_surface = -GMm/R. Calculate the change in potential energy when the mass is raised to height h = R.

1. GMm/(R+h)
2. GMm/(R²)
3. GMm/(R+h)²
4. GMm/(R)

Correct answer: GMm/(R+h)

Solution

The potential energy at height h = R is U_h = -GMm/(R + h) = -GMm/(2R). The change in potential energy is ΔU = U_h - U_surface = [-GMm/(2R)] - [-GMm/R] = GMm/(2R). Thus, the correct answer is A.

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