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 , as sho

Question

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 , as shown in figure, the bead is at rest with respect to the circular ring at position  as shown. Then the value of  is equal to :

Canvas Classes · Accepted Answer

🧠 Bead on Rotating Vertical Ring — Tangential Force Balance

A bead sits on a smooth circular wire that rotates about its vertical diameter. In the rotating frame, the bead is at rest if the tangential component of (gravity + centrifugal force) is zero.

Let the bead be at angle  from the downward vertical (measured at the centre of the ring). Position from centre: radius  outward at this angle.

Tangential force balance (along the wire's local tangent):

For the position  shown (at  from

More questions from this chapter

More questions from this chapter