2019 GravitationGravitational Potential Energy Medium Question 1 of 5 in Gravitational Potential Energy

The work done to raise a mass $m$ from the surface of the earth to a height $h$, which is equal to the radius of the earth, is:

A $mgR$
B $2\,mgR$
C $\frac{1}{2}mgR$
D $\frac{3}{2}mgR$

The answer is C.

Solution

Initial potential energy at the earth's surface: $U_i=-\frac{GMm}{R}$ Final potential energy at height $h=R$: $U_f=-\frac{GMm}{2R}$ Work done = change in PE: $W=U_f-U_i=\frac{GMm}{2R}$ Using $GM=gR^2$: $W=\frac{gR^2m}{2R}=\frac{1}{2}mgR$

Concept work to raise a mass to a height equal to R

Gravitational Potential Energy in past papers

5 questions from this chapter have appeared across 4 exam years.