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

QB_PH_048: Central force problem

Question Statement

Using Binet's equation $\frac{d^2 u}{d\theta^2} + u = -\frac{m}{L^2 u^2} F(1/u)$, an attractive force $F(r) = -k/r^3$ leads to an orbit of the form:
(A) u = A \cos(\beta \theta + \delta)
(B) u = A \theta + B
(C) u = A e^{\beta \theta}
(D) u = A \tan(\theta)
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Binet equation becomes $\frac{d^2 u}{d\theta^2} + (1 - mk/L^2)u = 0$, giving harmonic solutions.
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