Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table.

Solution:

0;

$-2.7 \times 10^{-8} \mathrm{~J} / \mathrm{kg}$

Yes;

Unstable

Explanation:

The situation is represented in the given figure:

Mass of each sphere, M = 100 kg

Separation between the spheres, r = 1m

X is the mid point between the spheres. Gravitational force at point X will be zero. This is because gravitational force exerted by each sphere will act in opposite directions.

Gravitational potential at point X:

$=\frac{-\mathrm{G} M}{\left(\frac{r}{2}\right)}-\frac{\mathrm{G} M}{\left(\frac{r}{2}\right)}=-4 \frac{\mathrm{G} M}{r}$

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

$=-2.67 \times 10^{-8} \mathrm{~J} / \mathrm{kg}$

Any object placed at point X will be in equilibrium state, but the equilibrium is unstable. This is because any change in the position of the object will change the effective force in that direction.