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 axes 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

B

Explanation

Kinetic energy of rotation, `K_(R)=1/2Iomega^(2)`
or `omega^(2)=(2K_(R))/I`
Since `K_(R)` remains the same for all three configurations,
`thereforeomegaprop1/(sqrtl)`
Let m be the mass and a be side of each square plate
In figure 1, moment of inertia about the given axis,

`I_(1)=1/12ma^(2)`
In figure 2, moment of inertia about
the given axis,
`I_(2)=1/12ma^(2)`

In figure 3, moment of inertia
about the given axis
`I_(3)=1/6ma^(2)`
`thereforeI_(1):I_(2):I_(3)=1:1:2`
As `omegaprop1/(sqrtl)`
`thereforeomega_(1):omega_(2):omega_(3)=1:1:1/(sqrt2)=sqrt2:sqrt2:1`