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  • Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

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 Moment of Inertia is given by I=\sum m_{i}r_{i}^{2} where r is the distance of the mass from the axis of rotation. In solid sphere entire mass is distributed from centre to the radius of the sphere whereas in a hollow sphere whole mass is concentrated at the periphery of the sphere. Thus in hollow sphere average value of r_{i} becomes larger and hence results in a greater moment of Inertia.

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