Q120 / 180 · AIIMS 2013 · Physics

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
    $-g(R+h)$
  • Correct answer
    B
    $-g(R-h)$
  • C
    $g(R+h)$
  • D
    $g(R-h)$

Solution

If a point mass m is placed at a height h from surface of earth, the potential energy is $U_h=-\frac{G M m}{(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{G M}{R^2}\right)$ $U_h=\frac{-g R^2 m(R-h)}{R^2}$ $=-g m(R-h)$ $\therefore \quad V=\frac{U_h}{m}=\frac{-g m(R-h)}{m}=-g(R-h)$

Hence, the correct answer is option: 'B'.

More Gravitation Questions