Moment Of Inertia Of A Solid Sphere - Practice Questions & MCQ

Let I=Moment of inertia of a SOLID SPHERE about an axis through its centre

To calculate I

Consider a sphere of mass M, radius R and centre O. Mass per unit volume of the sphere =  

Take an elementary disc of mass dm, whose centre is C and which lies between two planes perpendicular to the axis at a distance x and x + dx from its centre

Disc has Radius=AC and thickness =dx.  As shown in figure

So,  

So,   

The moment of inertia of the elementary  disc about the axis

 Now integrate this dI  between the limits x=-R to x=+R