# A particle of mass 10 g is kept on surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work done against gravitational force between them, to take the particle for away from sphere $(G=6.67 \times 10^{-11} Nm^2/kg)$

$(a)\;3.33 \times 10^{-10} \;J \quad (b)\;13.34 \times 10^{-10}\;J \quad (c)\; 6.67 \times 10^{-9}\;J \quad (d)\;6.67 \times 10^{-10}\;J$

$\Delta W= Work done=v_f-u_i$
$\qquad= 0 -\bigg[\large\frac{-GMm}{R}\bigg]$
$\Delta W=\large\frac{6.67 \times 10^{-11} \times 100}{0.1} \times \frac{10}{1000}$
$\qquad= 6.67 \times 10^{-10}J$
hence d is the correct  answer.

edited Feb 17, 2014 by meena.p