Physics - Gravitation Question with Solution | TestHub

Force on the body$=\frac{GMm}{x^2}$

To move it by a small distance$dx$,

Work done$=F dx=\frac{GMm}{x^2}dx$

Total work done$=GMm \underset{R}{\overset{R+h}{\int }}\frac{dx}{x^2}={\left[\frac{-GMm}{x}\right]}_R^{R+h}$

$=GMm\left[\frac{1}{R}-\frac{1}{R+h}\right]$

$=\left[\frac{\left(R+h\right)-R}{R(R+h)}\right]=\frac{GMmh}{R(R+h)}$

$\frac{GM}{R^2}\times \frac{mhR}{R+h}=\frac{\mathrm{g}mhR}{R+h}=\frac{PRh}{R+h}$