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A small bead of mass m is carried by a c...

A small bead of mass `m` is carried by a circular hoop having center at `O` and radius `sqrt 2m` which rotates about a fixed vertical axis. The coefficient of friction between beed and hoop is `mu=0.5`. The maximum angular speed of the hoop for which the bead does not have relative motion with respect to hoop. `(g=10m//s^(2))`

A

`sqrt5`

B

`sqrt10`

C

`sqrt15`

D

`sqrt30`

Text Solution

Verified by Experts

The correct Answer is:
D
The maximum angular speed of the hoop corresponds to the situations when the bead is just about to slide upwards. For the bead to slide upwards.
`cos45^(0)=x/r rArr x=r cos45^(0)`
`m omega^(2) (r sin 45)-mg sin 45 le muN`
Where `N=mg cos 45 + momega^(2) (r sin45) sin 45`
On solving `omega le sqrt(((1+mu)g)/((1-mu)r sin 45))`
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