Question

In the figure shown below, a solid sphere of radius $5\text{m}$ is arranged concentrically with a hollow sphere of radius $9\text{m}$. Find the moment of inertia of the system about an axis passing through their centre. (Take $m_s=$ mass of solid sphere $=5\text{kg},m_h=$ mass of hollow sphere $=3\text{kg}$).

• A. $202{\text{kg-m}}^2$
• B. $212{\text{kg-m}}^2$
• C. $162{\text{kg-m}}^2$
• D. $81{\text{kg-m}}^2$

Answer 1

The correct option is B $212{\text{kg-m}}^2$

Given, radius of solid sphere $\left(r_s\right)=5\text{m}$
Radius of hollow sphere $\left(r_h\right)=9\text{m}$
Moment of inertia of solid sphere $I_s=\frac{2}{5}{m}_s{r}_s^2$
$=\frac{2}{5}\times 5\times (5{)}^2$
$=50{\text{kg-m}}^2$

Moment of inertia of hollow sphere $I_h=\frac{2}{3}{m}_h{r}_h^2$
$=\frac{2}{3}\times 3\times (9{)}^2$
$=162{\text{kg-m}}^2$

Total moment of inertia about axis passing through centre
$\left(I\right)=I_s+I_h=212{\text{kg-m}}^2$