A rod of length 50cm is pivoted at one end. It is raised such that if makes an angle of `30^(@)` from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad`s^(-1)`) will be (`g=10ms^(-2)`)

Options

A. `sqrt(30/2)`
B. `sqrt(30)`
C. `sqrt(30)/2`
D. `sqrt(20)/3`

Answer

B

Explanation

`W = DeltaKE, mg l/2 sin 30^(@) = 1/2 I_("hinge")omega^(2)`,
`mg /2 xx 1/2 =1/2(ml^(2))/3 omega^(2)`
`rArr omega = sqrt((3g)/(2l)) = sqrt((3 xx 10)/(2 xx 1/2)), omega = sqrt(30) rad//s`.