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

Two bodies have their moments of inertia I and 2I, respectively about

1.	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
Answer» `2:1` `1:2` `sqrt(2):1` `1:sqrt(2)` SOLUTION :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`.