Two heavy spheres, each of mass $100 ext{ kg}$, are placed $1.0 ext{ m}$ apart. An object is place

Question

Two heavy spheres, each of mass $100	ext{ kg}$, are placed $1.0	ext{ m}$ apart. An object is placed at the mid-point of the line joining their centres. What is the net gravitational force on the object, and what is the nature of its equilibrium along the line joining the centres?

Professor PC Thomas Classes · Answer

At the exact mid-point, the gravitational pulls from both spheres are equal and opposite, resulting in a net force of zero (equilibrium). If the object is displaced slightly towards either sphere, the pull from the closer sphere becomes stronger, pulling it further away from the mid-point. Thus, the equilibrium is unstable.