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Q.

A body of mass M is raised from the surface of the earth to an altitude equal to the radius of the earth. The potential energy gained by the body will be

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a

$\frac{MgR}{2}$

b

$MgR$

c

$\frac{3 MgR}{2}$

d

2 MgR

answer is A.

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Detailed Solution

Given,

Question Image

Here m is mass of earth M is mass of body

$U_{1} = - \frac{GMm}{R} U_{f} = - G \frac{Mm}{R + h} h = R$

$U_{f} = - \frac{GMm}{R + R} = - G \frac{Mm}{2 R}$

$Δ U = U_{f} - U_{i}$

$= - G \frac{Mm}{2 R} + G \frac{Mm}{R} = \frac{- GMm + 2 GMm}{2 R}$

$\begin{aligned} = \frac{GMm}{2 R} (g = \frac{Gm}{R^{2}}) \\ = \frac{{gR}^{2} \times M}{2 R} = \frac{MgR}{2} \end{aligned}$

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A body of mass M is raised from the surface of the earth to an altitude equal to the radius of the earth. The potential energy gained by the body will be