Moment Of Inertia

To calculate the moment of inertia of a spherical shell with inner radius and outer radius , we need to use the integral formula for the moment of inertia of a continuous mass distribution: where is the distance from the axis of rotation, and is the mass element of the shell.
The spherical shell has a uniform mass distribution. The mass element of a thin spherical shell of radius and thickness is given by: Thus, the total moment of inertia of the spherical shell is: Integrating , we get: Thus, the moment of inertia is: Thus, the correct answer is .