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{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. $