Question

Moment of inertia of a thin spherical shell of mass M and radius R, about its diameter is
1. \(MR^2\)
2. \(\frac{1}{2}MR^2\)
3. \(\frac{2}{5}M{R^2}\)
4. \(\frac{2}{3}M{R^2}\)

Answer 1

Correct Answer - Option 4 : \(\frac{2}{3}M{R^2}\)

Explanation:

Moment of inertia:

Moment of inertia is a measure of the resistance of a body to angular acceleration about a given axis that is equal to the sum of the products of each element of mass in the body and the square of the element’s distance from the axis.

I = ∑( m₁r₁² + m₂r₂² + m₃r₃² +m₄r₄² + …….. + m_nr_n²)

Moment of inertia of a thin spherical shell of mass M and radius R about its diameter.

\({\rm{I}} = \frac{2}{3}{\rm{M}}{{\rm{R}}^2}\)

Moment of inertia of some important shapes:

Body	Axis of Rotation	Moment of inertia
Uniform circular ring of radius R	Perpendicular to its plane and through the centre	MR2
Uniform circular ring of radius R	About diameter	\(\frac{MR^2}{2}\)
Uniform circular disc of radius R	Perpendicular to its plane and through the centre	\(\frac{MR^2}{2}\)
Uniform circular disc of radius R	About diameter	\(\frac{MR^2}{4}\)
A solid cylinder  of radius R	Axis of the cylinder	\(\frac{MR^2}{2}\)
A hollow cylinder of radius R	Axis of cylinder	MR2