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 symmentry ?

Why does a solid sphere have smaller moment of inertia than a hollow c

1.	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 symmentry ?
Answer» By definition, `I = underset(i)sum m_(i)r_(i)^(2)` In case of hollow cylinder, entire lies at disatnce `R` from the axis of symmetry. But in case of a solid sphere, the same mass is distributed throughout at distance from zero to `R` from the axis of symmetry. Here, `R` is radius of cylinder/sphere. That is why a solid sphere has smaller moment of inertia than a hollow cylinder of same mass and radius.

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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 symmentry ?

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