Length, width and mass of a rectangular plate are $ \ell, \mathrm{b} $ and $ \mathrm{m} $ respectively. The radius of gyration about the axis passing through centre and perpendicular to the plane is :

Question

Length, width and mass of a rectangular plate are $ \ell, \mathrm{b} $ and $ \mathrm{m} $ respectively. The radius of gyration about the axis passing through centre and perpendicular to the plane is :, $ \sqrt{\frac{\ell^{2}+\mathrm{b}^{2}}{2}} $, $ \sqrt{\frac{\ell^{2}+\mathrm{b}^{2}}{8}} $, $ \sqrt{\frac{\ell^{2}+\mathrm{b}^{2}}{12}} $, $ \sqrt{\frac{\ell^{2}+b^{3}}{12}} $

MARKS App · Accepted Answer

Moment of inertia of a rectangular plate about an axis passing through its centre and perpendicular to the plane is given by I = m l 2 + b 2 12 . . . . 1 As radius of gyration k is given by using the expression I = m k 2 So, k = I m ⇒ k = l 2 + b 2 12 .

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