Question

A body of mass m is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

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

Answer 1

The correct option is D $\frac{2}{3}mgR$

From work-energy theorem, work done = change in potential energy.

Work done = ${\int }_R^{3R}\frac{GmM}{x^2}dx=\frac{2GmM}{3R}=\frac{2mgR}{3}$.

Please note that the gravitational force will necessarily vary over this height because it is comparable with earth's radius.