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(A) The gravitational potential energy of a body of mass $m$ at the surface of the earth is given by $U_1 = -\frac{G M m}{R}$.At a height $h = \frac{R

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$\frac{G M m}{4 R}$

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(A) The gravitational potential energy of a body of mass $m$ at the surface of the earth is given by $U_1 = -\frac{G M m}{R}$.At a height $h = \frac{R}{3}$ above the surface,the distance from the center of the earth is $r = R + h = R + \frac{R}{3} = \frac{4R}{3}$.The gravitational potential energy at this height is $U_2 = -\frac{G M m}{r} = -\frac{G M m}{4R/3} = -\frac{3 G M m}{4R}$.The work done in raising the body is equal to the change in gravitational potential energy:$W = U_2 - U_1 = \left( -\frac{3 G M m}{4R} \right) - \left( -\frac{G M m}{R} \right)$.$W = \frac{G M m}{R} - \frac{3 G M m}{4R} = \frac{4 G M m - 3 G M m}{4R} = \frac{G M m}{4R}$.

Work done in raising a body of mass $m$ from the surface of the earth to a height $\frac{R}{3}$ is ......... (where,$R$ is radius of earth,$M$ is mass of the earth and $G$ is gravitational constant)

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