Question Bank MCQ • 2 Marks Section 2: Classical Mechanics Classical Mechanics - Module 4

QB_PH_033: Classical Mechanics - Module 4

Question Statement

A particle of mass $m$ moves in a potential $V(r, \theta, z) = \frac{1}{2} k r^2 + \alpha z$ in cylindrical coordinates. Which conjugate momentum is strictly conserved?
(A) p_\theta = m r^2 \dot{\theta}
(B) p_z = m \dot{z}
(C) p_r = m \dot{r}
(D) None
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: The coordinate $\theta$ is cyclic (absent from $L$), so conjugate momentum $p_\theta$ is conserved.
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