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If the acceleration due to gravity at Earth’s surface is g, what increase in potential energy does a body of mass m acquire when it is lifted from the Earth’s surface to a height equal to the Earth’s radius R?

1. 1/4 mgR
2. 1/2 mgR
3. 2mgR
4. mgR

Correct answer: 1/2 mgR

Solution

When a mass m is lifted to a height equal to the Earth's radius R, the potential energy gained is calculated using the formula for gravitational potential energy, which varies with distance from the center of the Earth. At this height, the effective gravitational force is reduced, leading to the increase in potential energy being 1/2 mgR.

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