Question

What is the moment of inertia of a hollow sphere of radius $3\text{m}$ and mass $2\text{kg}$ about an axis passing through the geometric centre of the sphere?

• A. ${\text{20 kg-m}}^2$
• B. ${\text{40 kg-m}}^2$
• C. ${\text{12 kg-m}}^2$
• D. ${\text{24 kg-m}}^2$

Answer 1

The correct option is C ${\text{12 kg-m}}^2$

Radius of shere;$R=3\text{m}$
Mass of sphere ;$M=2\text{kg}$
Moment of inertia of a hollow sphere about an axis passing through the geometric centre of the sphere $=\frac{2M{R}^2}{3}$
$\Rightarrow \frac{2\times 2\times 3^2}{3}{\text{= 12 kg-m}}^2$

$\therefore$ Moment of inertia of the sphere about as axis passing through its geometric centre = $12{\text{kg-m}}^2$