Two bodies have their moments of inertia `I` and `2I`, respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio

Options

A. `2:1`
B. `1:2`
C. `sqrt(2):1`
D. `1:sqrt(2)`

Answer

C

Explanation

Consider two bodies A and B are having moment of inertia `I and 2I`
`K_(A)=` Kinetic energy of rotation for the body `A = (1//2)I omega_(A)^(2)` where, `omega_(A)` is angular speed of the body A
`K_(B)`= Kinetic energy of rotation for the body `B = (1)/(2)(2I)omega_(B)^(2)`
According to the question, `K_(A)=K_(B)`
`rArr (1)/(2)I omega_(A)^(2)=(1)/(2)(2I)omega_(B)^(2)rArr omega_(A)^(2)=2 omega_(B)^(2)rArr((omega_(A))/(omega_(B)))^(2)=2`
`rArr (omega_(A))/(omega_(B))=sqrt(2)rArr omega_(A):omega_(B)=sqrt(2):1`.