Question Bank MCQ • 2 Marks Section 2: Classical Mechanics Small oscillations

QB_PH_043: Small oscillations

Question Statement

A pendulum of mass $m$ and length $l$ hangs from a cart of mass $M$ free to move horizontally. For small oscillations, the frequency is:
(A) \sqrt{\frac{g}{l} \frac{M + m}{M}}
(B) \sqrt{\frac{g}{l}}
(C) \sqrt{\frac{g}{l} \frac{M}{M + m}}
(D) \sqrt{\frac{g}{l} \frac{m}{M}}
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Eliminating the cyclic cart coordinate yields reduced mass dynamics with frequency $\omega = \sqrt{\frac{g}{l}\frac{M+m}{M}}$.
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