Question

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 1

Consider the diagram where an object of mass m is raised from the surface of the earth to a distance (height) equal to the radius of the earth (R).

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^2 xx m)/(2R)`

= `1/2 mgR`  ......(∵ Gm = gR²)