Potential energy of a system of particles is U=α3r3−β2r2, where r is distance between the particles. Here α and β are positive constants. Which of the following are correct for the system?
Equilibrium separation between the particles is αβ
For r=αβ, the equilibrium is stable
For r=αβ, the equilibrium is unstable
Work required to slowly move the particles to infinite separation from initial equilibrium position is βα
The correct options are
A Equilibrium separation between the particles is αβ
B For r=αβ, the equilibrium is stable
For equilibrium condition, F=0
⟹stable equilibrium (as P.E is minimum)
Work required to slowly move the particle from r=αβ to ∞
∴ Option A and B are correct.