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} $