Question

A small planet is between two stars of different masses and radii such that the net force on the planet is zero. On displacing the planet on either side, can it under go oscillatory motion?

• A. No, not at all
• B. Only if the displacement is small
• C. Yes definitely
• D. One can't surely say

Answer 1

The correct option is A No, not at all

At equilibrium $F_A=F_B$

But this equilibrium is unstable as the moment you displace the planet to one side the attraction force by the star on that side will increase and the planet will keep drifting that side. And hence the planet can't oscillate.