Question

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. $2mgR$
• C. $\frac{1}{2}mgR$
• D. $\frac{3}{2}mgR$

Answer 1

The correct option is C $\frac{1}{2}mgR$

Initial potential energy at earth's surface is
$U_i=\frac{-GMm}{R}$
Final potential energy at height $h=R$
$U_f=\frac{-GMm}{2R}$​
As work done = change in PE
$\therefore W=U_f-U_i=\frac{GMm}{2R}(\because GM=g{R}^2)$
= $\frac{g{R}^{2}m}{2R}=\frac{mgR}{2}$