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Question
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, then what is the ratio of their angular velocity.
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Solution
Given:
(K.E.)1 = (K.E.)2
∴ `1/2I_1omega_1^2 = 1/2I_2omega_2^2`
∴ `omega_1/omega_2 = sqrt((I_2)/(I_1))`
= `sqrt((2I)/I)` ..........(Given: I1 = I, I2 = 2I)
`omega_1/omega_2 = sqrt2/1`
∴ ω1 : ω2 = `sqrt2` : 1
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