Two heavy spheres each of mass $100 \; kg$ and radius $0.10 \; m$ are placed $1.0 \; m$ apart on a horizontal table. What is the gravitational force and potential at the mid-point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so,is the equilibrium stable or unstable?

(N/A) Mass of each sphere,$M = 100 \; kg$.
Separation between the centres of the spheres,$r = 1.0 \; m$.
Let $X$ be the mid-point between the centres of the spheres.
$1$. Gravitational Force at $X$:
The gravitational force exerted by each sphere on an object at $X$ is equal in magnitude but opposite in direction. Therefore,the net gravitational force at $X$ is $0 \; N$.
$2$. Gravitational Potential at $X$:
The gravitational potential $V$ at a distance $d$ from a mass $M$ is given by $V = -GM/d$. At the mid-point $X$,the distance from each sphere is $d = r/2 = 0.5 \; m$.
$V_{total} = V_1 + V_2 = -\frac{GM}{r/2} - \frac{GM}{r/2} = -\frac{4GM}{r}$
$V_{total} = -\frac{4 \times 6.67 \times 10^{-11} \times 100}{1.0} = -2.668 \times 10^{-8} \; J/kg \approx -2.67 \times 10^{-8} \; J/kg$.
$3$. Equilibrium:
Since the net force is zero,an object placed at $X$ is in equilibrium. If the object is displaced slightly towards one sphere,the gravitational force from that sphere increases while the force from the other decreases. This creates a net force in the direction of displacement,pulling the object further away from $X$. Thus,the equilibrium is unstable.