Question
A frictionless circular wire of unit radius is fixed on the horizontal plane. Two-point particles of unit mass start moving simultaneously from point $A\left( \theta = \frac{\pi}{2} \right)$ with identical uniform angular speeds in opposite directions, and meet again at point $B\left( \theta = - \frac{\pi}{2} \right)$. During this time, which of the following figures schematically represent the magnitude of the total linear momentum $P$ of the system, as a function of $\theta$ ?
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Solution
Sol. [Key Concept: Dynamics of beads on a circular wire]
$${\ \begin{matrix} & {\overrightarrow{P}}_{net} = - mvsin\theta\widehat{i} - mvcos\theta\widehat{j} + mvsin\theta\widehat{i} - mvcos\theta\widehat{j} \\ & {\overrightarrow{P}}_{net} = - 2mvcos\theta\widehat{j} \\ & \text{~}\text{at}\text{~}\theta = \frac{\pi}{2},{\overset{˙}{P}}_{net} = 0,\text{~}\text{at}\text{~}\theta = - \frac{\pi}{2},{\overset{˙}{P}}_{net} = 0 \end{matrix} } {So\ most\ appropriate\ graph\ is }$$
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