Question

Two particles of identical mass are moving in circular orbits under a potential given by V(r) = Kr^-n, where K is a constant. If the radii of their orbits are r₁.r₂. and their speeds are v₁.v₂, respectively. Then,

(a) v₁² r₁ⁿ = v₂² r₂ⁿ

(a) v₁² r₁^-n = v₂² r₂^-n

(a) v₁² r₁ = v₂² r₂

(a) v₁² r₁^2-n = v₂² r₂^2-n

Answer 1

Answer is : (a) v₁² r₁ⁿ = v₂² r₂ⁿ

Given,

Potential, V = Kr^-n

So, magnitude of field,

As particles are rotating in circular path,