A small bead of mass 'm' is threaded on a frictionless circulat wire of radius 'a' . The circule wire frame is rotated about its vertical diameter as shown. (assume acceleration due to grasvity is g) The angular speed required if the bead is to be made to move in a horizontal circle of radius `(a sqrt(3))/(2)` is :

Options

A. `((g)/(a))^(1//2)`
B. `((2g)/(a))^(1//2)`
C. `((3g)/(2a))^(1//2)`
D. `((3g)/(a))^(1//2)`

Answer

B

Explanation

A small bead …………….
`N sin theta = mg`
`N cos theta = m omega^(2)(a sqrt(3))/(2)`

When friction in absent :
`:. Tan theta = (2g)/(omega^(2)a sqrt(3)) = (1)/(3)`
`omega = ((2g)/(a))^((1)/(2))`