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State the formula for moment of inertia of a solid sphere and hollow sphere about its diameter.

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Last updated date: 20th Jun 2024
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Answer
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Hint:We are to write the formula for moment of inertia of a solid sphere and a hollow sphere. First know the meaning of the moment of inertia. Then recall the formula for moment of inertia of a solid sphere and a hollow sphere, write down the formula by stating each term of the formula.

Complete answer:
First let us know what moment of inertia is. Moment of inertia is a quantity that expresses a body’s tendency to resist angular acceleration.Now, let us write the formula for the moment of inertia of a solid sphere. The moment of inertia for a solid sphere is a,
\[{\left( {M.I} \right)_{{\text{solid}}\,{\text{sphere}}}} = \dfrac{2}{5}M{R^2}\]
where \[M\] is the mass of the solid sphere and \[R\] is the radius of the solid sphere.
Now, we will write the formula for the moment of inertia of a hollow sphere. The moment of inertia of a hollow sphere is,
\[{\left( {M.I} \right)_{{\text{hollow}}\,{\text{sphere}}}} = \dfrac{2}{3}M{R^2}\]
where \[M\] is the mass of the hollow sphere and \[R\] is the radius of the hollow sphere.

Therefore, the formula for moment of inertia for solid and hollow sphere is \[\dfrac{2}{5}M{R^2}\] and \[\dfrac{2}{3}M{R^2}\] respectively.

Note: The formulas of moment of inertia of some important shapes should always be remembered which are the moment of inertia of the rectangle plate, solid and hollow cylinder, rod, solid and hollow sphere, circular ring. There are also two important theorems of finding moment of inertia about an axis, which are parallel axis theorem and perpendicular axis theorem.