Question

If the acceleration due to gravity at the surface of the earth is $g$, the work done in slowly lifting a body of mass $m$ from the earth's surface to a height $R$ equal to the radius of the earth is

• A. $\frac{mgR}{2}$
• B. $2mgR$
• C. $mgR$
• D. $mg\frac{R}{4}$

Answer 1

The correct option is A $\frac{mgR}{2}$

$\begin{array}{c}{u}_i=\frac{GM}{R}=mgR\\ u_f=\frac{GMm}{2R}\\ =\frac{GM}{R^2}.\left(\frac{MR}{2}\right)\\ =\frac{mgR}{2}\\ \therefore w=\frac{mgR}{2}\end{array}$

$\therefore$ Option $C$ is correct .