A thin circular wire of radius rotates about its vertical diameter with angular frequency

PHYSICS · Subjective · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A thin circular wire of radius rr rotates about its vertical diameter with angular frequency ω\omega. Show that a small bead on the wire remains at its lowest point for ω≤g/r\omega\leq\sqrt{g/r}. What angle does the radius vector joining the centre to the bead make with the vertically downward direction for ω=2g/r\omega=\sqrt{2g/r}? Neglect friction.

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