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An object of mass m is raised from the s...

 An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy ?

Text Solution

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 Potential energy of the object at the surface of the earth = `-(GMm)/R`
PE of the object at a height equal to the radius of the earth `=-(GMm)/(2R)`
`:.` Gain in PE of the object
`=(-GMm)/(2R) -(-(GMm)/R)`
`=(-GMm+2GMm)/(2R) = +(GMm)/(2R)`
`= (gR^2xxm)/(2R) = 1/2 mgR " " ( :. g = (GM)/(R^2))`
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