Question

A ring of radius R lies in vertical plane. A bead of mass ‘m’ can move along the ring without friction. Initially the bead is at rest at the bottom most point on ring. The minimum constant horizontal speed v with which the ring must be pulled such that the bead completes the vertical circle.

(A) √3gR

(B) √4gR

(C) √5gR

(C) √5gR

Answer 1

Correct option: (B) √4gR

Explanation:

In the frame of ring (inertial w.r.t. earth), the initial velocity of the bead is v at the lowest position.

The condition for bead to complete the vertical circle is, its speed at top position 

v_top ≥ 0

From conservation of energy