A uniform solid sphere has a radius 0.1 m and density ` 6 xx 10 ^ 3 ` kg/ `m^ 3 ` . Find the moment of intertia about a tangent to its surface.

Explanation

Given : Radius of solid sphere (R )
` = 0.1 m`
Density ( ` rho ` ) = ` 6 xx 10 ^ 3 kg // m^ 3 `
Mass of the sphere (M ) = volume ` xx ` density
` = ( 4)/(3) pi R^ 3 rho `
Moment of inertia about a tangent to its surface,
` I = (2 ) /( 5 ) MR ^ 2 + MR ^ 2 `
[ Using parallel axis theorem ]
` I = ( 7 )/( 5 ) MR^ 2 `
` = ( 7 ) /( 5 ) xx (4 )/( 3) xx pi xx R^3 xx rho xx R^ 2 `
` = ( 28 xx 3.14 xx 6 xx 10 ^ 3 xx ( 0.1 ) ^ 5 ) /( 15 ) `
` therefore I = 0.3517 kg m^ 2 `