Question

An object of mass m is raised from the surface of the earth to a height of 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 1

Given : An object is raised distance R → 2R

Potential energy of body on the surface of earth = \(\frac{-GMm}{R}\)

P.E. of object at height equal to radius of earth = \(\frac{-GMm}{2R}\)

Gain in Potential Energy= P.E_f - P.E_i

= \(\frac{GMm}{R}\) - GMmR

= \(\frac{GMm}{R}\)\(\Big[-\frac{1}{2}+1\Big]\)

= \(\frac{GMm}{2R}\)

As, GM = gR²

Gain in P.E. = \(\frac{gR^2m}{2R}\) = \(\frac{1}{2}mgR\)