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If a thin circular ring and a thin flat circular disk of same mass have same moment of inertia about their respective diameters as axis. Then find the ratio of their radii.

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Moment of inertia of a thin circular ring about its diameter is, `I_1 = m_1R_1^2`
Moment of inertia of a flat circular disc about its diameter is `I_2 = (m_2R_2^2)/(2)`
Given that two objects having same moment of inertia i.e., `I_1 = I_2`
`rArr m_1 R_1^2 = (m_2R_2^2)/(2)`
Given that `m_1 = m_2` hence `R_1^2 = (R_2^2)/(2)` ltbrlt `rArr (R_2^2)/(R_2^2) =1/2 " or " R_1/R_2 = 1/sqrt2`
`therefore` Ratio of radii , `R_1 : R_2 = 1 1 : sqrt2`
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