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A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be:

1. 2/3 mgR
2. 3 mgR
3. 1/3 mgR
4. mg2R

Correct answer: 2/3 mgR

Solution

The change in gravitational potential energy is given by ΔU = -GMm(1/r2 - 1/r1). Here, r1 = R (radius of Earth) and r2 = 3R (R + 2R). Substituting, ΔU = -GMm(1/3R - 1/R) = GMm(2/3R). Using GM = gR^2, ΔU = 2/3 mgR.

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