A smooth wire of length 2 π r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter A

Question

A smooth wire of length 2 π r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter A B , as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω 2 is equal to:

TestHub · Accepted Answer

From free body diagram of bead, N c o s 30 ° = m g .... (1) N s i n 30 ° = m r 2 ω 2 ..... (2) By dividing equation (2) by equation (1) t a n 30 ° = r ω 2 2 g ω 2 = 2 g r 3

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