Question

The work done in shifting a particle of mass $m$ from the centre of the earth to the surface of the earth is (Where $M$ is the mass of the earth and $R$ is the radius of the earth)

• A. $- \frac{GMm}{R}$
• B. $+ \frac{GMm}{R}$
• C. $+ \frac{GMm}{2R}$
• D. $- \frac{GMm}{2R}$

Answer 1

Answer: (C)

Gravitational potential energy at the centre of the earth is
$u_{i} = -\frac{3GMm}{2R} $
Gravitational potential energy at the surface of the earth is
$u_{f} = -\frac{GMm}{R} $
Work done, $W = U_{f} - U_{i} $
$ = -\frac{GMm}{R} -\left(- \frac{3Gm}{2R}\right)$
$ W = - \frac{GMm}{R} + \frac{3GMm}{2R} $
$ = + \frac{GMm}{2R}$