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Q.

If g is acceleration due to gravity on the Earth's surface, the gain in the potential energy of an object of mass m raised from the surface of Earth to a height equal to the radius R of the earth is

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a

12mgR

b

2mgR

c

mgR

d

14mgR

answer is A.

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Detailed Solution

At a distance x from the centre of earth, the gravitational forceF=GMmx2dW=Fdx=GMmx2dx We get W=∫RR+h GMmx2dx=GMm1R−1R+h =gR2m1R−1R+hTherefore, the gain in potential energy isgR2m1R−12R=mgR2
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If g is acceleration due to gravity on the Earth's surface, the gain in the potential energy of an object of mass m raised from the surface of Earth to a height equal to the radius R of the earth is