# A smooth wire of length  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  about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then value of  is equal to:Option 1)Option 2)Option 3)Option 4)

from geometry

equating (1) and (2)

Option 1)

Option 2)

Option 3)

Option 4)

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