In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is sqrt2.5. Its radius of gyration about a tangent in its plane (in the same unit) must be ______.

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In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is sqrt2.5. Its radius of gyration about a tangent in its plane (in the same unit) must be 2.5. Explanation: The expression for the M.I. of a uniform disc about its central and transverse axis is given by M.I = (m xx R^2)/2 ......(i) Here, m and R are mass and radius of gyration, respectively. Let K be the radius of gyration of the disc. Then, from (i) we can write, M.I = (m xx R^2)/2 m xx K^2 = (m xx R^2)/2 K = R/sqrt(2) Therefore, sqrt2.5 = R/sqrt(2) R = sqrt(5) ......(ii) Now, the expression for the moment of inertia of a uniform disc about a tangent is given by M.I = (5 m R^2)/4 If K' be the radius of gyration of the disc about the tangent, then we can write M.I = (5 m R^2)/4 m $\times$ (K')2 = (5 m R^2)/4 (K')2 = (5 R^2)/4 (K')2 = (5(sqrt 5)^2)/4 (K')2 = (5 xx 5)/4 (K')2 = $\frac{25}{4}$ (K') = 2.5

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