Question

Two solid spheres of iron have their radii in the ratio $2:1$ . Then ratio of the moments of inertia about their diameters is :

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

Answer 1

The correct option is D $32:1$

The moment of inertia is given as,

$I=\frac{2}{5}M{R}^2$

$I=\frac{2}{5}\times \frac{4}{3}\pi R^3\times \rho \times R^2$

$I\propto R^5$

$\frac{I_1}{I_2}={\left(\frac{R_1}{R_2}\right)}^5$

The ratio of moments of inertia about their diameters is given as,

$\frac{I_1}{I_2}={\left(\frac{2}{1}\right)}^5$

$\frac{I_1}{I_2}=\frac{32}{1}$