Question

Two solid spheres of iron have radii in the ratio 1 : 2, their moments of inertia will be in the ratio:

• A. 1 : 32
• B. 1 : 16
• C. 1 : 8
• D. 1 : 4

Answer 1

Answer: (A)

From the formula the moment of inertia of sphere is $I=\frac{2}{5}m{r}^2$ where $m=\frac{4}{3}\pi r^3\rho$ where $\rho$ is the density of the body so, $I=\frac{2r^2}{5}\times \frac{4}{3}\pi r^3\rho =\frac{8}{15}\pi \rho r^3$ $I\propto r^5$ Therefore, moment of inertia is proportional to $r^5$ . Hence ratio will be $1:2^5=1:32.$