Question

Gravitational potential of the body of mass m at a height h from surface of earth of radius R is (Take g = acceleration due to gravity at earth’s surface)

• A. -g(R + h)
• B. -g(R - h)
• C. g(R + h)
• D. g(R - h)

Answer 1

Answer: (B)

If a point mass $m$ is placed at a height $h$ from surface of earth, the potential energy is
$U_h=-\frac{GMm}{(R+h)}=\frac{-g{R}^{2}m}{R\left(1+\frac{h}{R}\right)}=\frac{-g{R}^{2}m}{R}{\left(1+\frac{h}{R}\right)}^{-1}$
$\left(\because g=\frac{GM}{R^2}\right)$
$U_h=\frac{-g{R}^{2}m(R-h)}{R^2}$
$=-gm(R-h)$
$\therefore V=\frac{U_h}{m}=\frac{-gm(R-h)}{m}=-g(R-h)$