Q: The work done in lifting particle of mass m from the centre of earth to the surface of the earth is

(a) –mgR

(b) (1/2) mgR

(c)Zero

(d) mgR

Sol: (b)

$ \displaystyle U_1 = -\frac{3 G M m}{2R} $

$ \displaystyle U_2 = -\frac{G M m}{R} $

$ \displaystyle U_2 – U_1 = \frac{G M m}{R} (\frac{3}{2}-1) $

$ \displaystyle = \frac{G M m}{2R} $

$ \displaystyle = \frac{g R^2 m}{2R} $

$\displaystyle = \frac{m g R}{2} $