Q: Two heavy spheres each of mass 100Kg and radius. 0.1m are placed 1m apart on a horizontal table. What is the gravitational field and potential at the midpoint of the line joining their centres.

Sol: Gravitational field at the midpoint of the line joining their centres is given by

$\large E = \frac{GM}{(r/2)^2} – \frac{GM}{(r/2)^2} $

E = 0

Gravitational potential t the midpoint of the line joining their centres is given by

$\large V = -(\frac{GM}{(r/2)} + \frac{GM}{(r/2)} $

$\large V = -\frac{4GM}{r}$

$\large V = -\frac{4 \times 6.67 \times 10^{-11}\times 100}{1}$

=-2.7 × 10^{-8} j/kg.