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 ?

An object of mass m is raised from the surface of the earth to a heigh

1.	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 ?
Answer» Solution : Potential energy of the OBJECT at the surface of the earth = `-(GMM)/R` PE of the object at a height EQUAL to the radiusof 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))`