Answer
The work done by the net gravitational force on sphere B due to sphere A and sphere C is $~~-5.0\times 10^{-13}~J$
Work Step by Step
We can find the change in gravitational potential energy of the system:
$\Delta U_g = (-\frac{GM_AM_B}{2d}-\frac{GM_CM_B}{d})-(-\frac{GM_AM_B}{d}-\frac{GM_CM_B}{2d})$
$\Delta U_g = \frac{GM_AM_B}{2d}-\frac{GM_CM_B}{2d}$
$\Delta U_g = \frac{GM_B}{2d}~(M_A-M_C)$
$\Delta U_g = \frac{(6.67\times 10^{-11}~N~m^2/kg^2)(0.010~kg)}{(2)(0.040~m)}~~(0.080~kg-0.020~kg)$
$\Delta U_g = 5.0\times 10^{-13}~J$
The work done by the net gravitational force on sphere B due to sphere A and sphere C is equal to $~~-\Delta U_g$
Therefore, the work done by the net gravitational force on sphere B due to sphere A and sphere C is $~~-5.0\times 10^{-13}~J$
