Question Bank MSQ • 2 Marks Section 2: Classical Mechanics Central force problem

QB_PH_044: Central force problem

Question Statement

For a particle in an attractive central potential $V(r) = -k / r^n$ ($k > 0$), circular orbits are stable if and only if:
(A) n < 2
(B) n > 0
(C) n > 2
(D) n = 1 (Newtonian/Coulomb potential)
Correct Answer
A, B, D
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Stability requires $d^2 V_{eff}/dr^2 > 0$, which holds for $n < 2$.
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