Vertical Circle

Classical Mechanics Level 4

A wire is shaped in form of circular arc of a fixed radius as shown in the figure (\(0<\theta <\frac { \pi }{ 2 } \)). A small mass is given horizontal velocity \(v\) from point O such that it travels on this smooth wire and reaches point A and then travels in the air to reach point B. Find the value of \(\theta\) such that \(v\) is minimum.

If \(\theta\) can be represented as \(\frac{\pi}{n}\), select \(n\).

This problem is originally part of set Mechanics problems by Abhishek Sharma.

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