Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axis passes through the centre of the square. Then, the ratio of angular speeds `omega_(1):omega_(2):omega_(3)` is

Options

A. `1:1:1`
B. `sqrt2:sqrt2:1`
C. `1:sqrt2:1`
D. `1:2:sqrt2`

Answer

A

Explanation

We know that, `K=(1)/(2)l omega^(2)`
`"So, "omega prop (1)/(sqrt(l_(1)))`
`omega_(1):omega_(2):omega_(3)=(1)/(sqrt(l_(1))):(1)/(sqrt(l_(2))):(1)/(sqrt(l_(3)))`
`=(1)/(sqrt1):(1)/(sqrt1):(1)/(sqrt3)=sqrt2:sqrt2:1`