Question

Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the mid-point of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.

Answer 1

Given: m₁ = m₂ = M, r = 10R

Let mass m is placed at mid-point A (line joining the centres of P & Q sphere)

Now, |F₂| = |F₁| = \(\frac{GMm}{(5R)^2}\)

|F₂| = |F₁| = \(\frac{GMm}{25R^2}\)

F₁ & F₂ are equal and opposite forces are acting on m at A.

Net force F₁ = −F₂ or F₁ + F₂ = 0

So, mass is in equilibrium.

If m is slightly displaced from A to P then

AP = (5R – x)

AQ = (5R + x)

\(\therefore\) F₁ = \(\frac{GMm}{(5R-\mathrm x)^2}\) & F₂ = \(\frac{GMm}{(5R+\mathrm x)^2}\) or F₁ > F₂

That means resultant force acting on A is towards P. Hence, equilibrium is unstable equilibrium.