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  4. If g is the acceleration due to gravity on the earth's surface, the gain in potential energy of the body at a height equal to three times the radius R of the earth will be

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Q. If $g$ is the acceleration due to gravity on the earth's surface, the gain in potential energy of the body at a height equal to three times the radius $R$ of the earth will be

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Solution:

The gravitational potential energy at any point at a distance $x$ from the centre of earth is
$E=-\frac{GMm}{x}$
On the surface of earth $x = R$,
so, $E_{1}=\frac{-GMm}{R}=-mgR$
At a height $3R$, from the surface of earth, $x = 4R$
So, $E_{2}=\frac{-GMm}{4R}=-\frac{mgR}{4}$
Increase in potential energy,
$=-\frac{mgR}{4}+mgR=\frac{3}{4}mgR$