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A ring of radius R lies in vertical plan...

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 the bottom most point on ring. The minimum horizontal speed `v` with which the ring must be pulled such that the bead completes the vertical circle.

A

`sqrt(3gR)`

B

`sqrt(4 gR)`

C

`sqrt(5 gR)`

D

`sqrt(5.5 gR)`

Text Solution

Verified by Experts

The correct Answer is:
B
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")ge 0`
From conservation of energy
`1/2 m v_("top")^(2)+mg(2R)=1/2 mv^(2)`
or `v=sqrt(4gR)`
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