If g is the acceleration due to gravity on earth's surface, the gain in 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:

CONCEPT:

Gravitational Potential Energy: 

• The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force.
• The gravitational potential energy of a body at height h from the earth surface is given by

\(⇒ U=-\frac{GMm}{r}\)

Where M = mass of earth, m = mass of the body, r = distance from the earth

• The unit of Gravitational potential energy is Nm.
• The dimension of gravitational potential energy is  [ML2T-2].

CALCULATION:

• Initial gravitational potential energy is 

\(⇒ U_i=-\frac{GMm}{R}\)     ------- (1)

• Final gravitational potential energy is 

\(⇒ U_f=-\frac{GMm}{2R}\)     ------- (2)

• The gain in potential energy is 

⇒ ΔU = U_f - U_i

\(\Rightarrow \Delta U=(-\frac{GMm}{2R})-(-\frac{GMm}{R})=\frac{GMm}{2R}\)

As we know, 

\(\Rightarrow g = \frac{GM}{R^2}\)

\(\Rightarrow \Delta U=\frac{1}{2}mgR\)