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_ O and I_ P respectively. Both these axes are perpendicular to the plane of the lamina. The ratio I_ P / I_ O to the nearest integer is

Step-by-step solution

Let be the surface mass density. Moment of inertia of the lamina about axes passing through 'O' array l I_ O = 1 2 [ (2 R)² ] (2 R)²- = 13 2 R⁴ [ 1 2 ( R² )²+ ( R² ) R² ] array Moment of inertia of the lamina about axes passing through 'P' array l I_ P =8 R ⁴+ (2 R )² (2 R )² [ 1 2 ( R² ) R²+ ( R² ) ( (2 R)²+R² )² ] array array l =24 R ⁴-5.5 R ⁴=18.5 R ⁴ I_ P I_ O = 18.5 R⁴ 13 2 R⁴ = 37 13 3 array