Question

The moment of inertia of a hollow sphere of mass $1kg$ and inner and outer diameters $0.2$ and $0.4m$ respectively about its diametric axis will be :

• A. $Zero$
• B. $0.177kg/m^2$
• C. $0.0177kg/m^2$
• D. $177kg/m^2$

Answer 1

The correct option is C $0.0177kg/m^2$

For a hollow sphere of thickness we have the moment of inertia as $\frac{2m}{5}[\frac{r_2^5-r_1^5}{r_2^3-r_1^3}]$. Substituting the values we get $\frac{2}{5}[\frac{{0.2}^5-{0.1}^5}{{0.2}^3-{0.2}^3}]$
or
$\frac{2}{5}[\frac{(32-1)\times {10}^{-5}}{(8-1)\times {10}^{-3}}]$
or
$I=0.0177kg/m^2$