A lamina is made by removing a small disc of diameter 2 R from a bigger disc of uniform mass density and radius 2 R , as shown in the figure. The moment of inertia of this lamina about axes passing though O and P is I_

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Let σ be the surface mass density. Moment of inertia of the lamina about axes passing through 'O' array l I_ O =(1)/(2) σ[π(2 R)^ 2 ] ×(2 R)^ 2 - =(13)/(2) π σ R^ 4 [(1)/(2)(σ π R^ 2 )^ 2 +σ(π R^ 2 ) × R^ 2 ] array Moment of inertia of the lamina about axes passing through 'P' array l I_ P =8 π σ R^ 4 +σ π(2 R)^ 2 ×(2 R)^ 2 [(1)/(2) σ(π R^ 2 ) R^ 2 +σ(π R^ 2 )( (2 R)^ 2 +R^ 2 )^ 2 ] array array l =24 π σ R^ 4 -5.5 σ π R^ 4 =18.5 π σ R^ 4 I_ P I_ O = 18.5 π σ R^ 4 (13)/(2) π σ R^ 4 =(37)/(13) 3 array

A lamina is made by removing a small disc of diameter 2 R from a...

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