A spherical cavity is formed a solid sphere by removing mass from it. The resultant configuration is shown in figure. Find out the moment of inertia this configuration about the axis through centre of the solid sphere as shown . Take mass `M(` uniform `)` for the configuration and radius `R` for solid sphere and radius `R//2` for cavity.

Answer

`I=(57)/(140)MR^(2)`

Explanation

`rho=(M)/((4//3)piR^(3)-(4//3)pi(R//2)^(3))`
`I=(2)/(5)MR^(2)-((2)/(5)M_(2)((R)/(2))^(2)+M_(2)((R)/(2))^(2))`
`,I=(57)/(140)MR^(2)`