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  4. An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g =10 ms -2 and radius of earth =6400 km ]

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Q. An object of mass $1\, kg$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $g =10\, ms ^{-2}$ and radius of earth $=6400\, km$ ]

JEE MainJEE Main 2022Gravitation

Solution:

$ U _{ i }=\frac{- GMm }{ R } $
$ U _{ f }=-\frac{ GMm }{4 R } $
$ \Delta U = U _{ f }- U _{ i }=\frac{3 GMm }{4 R } $
$ =\frac{3}{4} mgR $
$=\frac{3}{4} \times 1 \times 10 \times 64 \times 10^5 $
$ =48\, MJ $