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)

1 : 32

Answer 2

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, $I=\frac{2{{r}^{2}}}{5}\times \frac{4}{3}\pi {{r}^{3}}\rho =\frac{8}{15}\pi \rho {{r}^{3}}$ $I\propto {{r}^{5}}$
Therefore, moment of inertia is proportional to ${{r}^{5}}$ .
Hence ratio will be $1:{{2}^{5}}=1:32.$
So, the correct option is (A): 1 : 32.