Question

The ratio of the radii of gyration of a spherical shell and a solid sphere of the same mass and radius about a tangential axis is:

• A. $\sqrt{3}:\sqrt{7}$
• B. $\surd 5:\surd 6$
• C. $\sqrt{25}:\sqrt{21}$
• D. $\sqrt{21}:\sqrt{25}$

Answer 1

The correct option is A $\sqrt{3}:\sqrt{7}$

Moment of inertia of a solid sphere about tangential axis is $\frac{2}{3}m{r}^2+m{r}^2=\frac{5}{3}m{r}^2$

Radius of gyration=$\sqrt{\frac{5}{3}}r$

Moment of inertia of a spherical shell about tangential axis is $\frac{2}{5}m{r}^2+m{r}^2=\frac{7}{5}m{r}^2$

Radius of gyration=$\sqrt{\frac{7}{5}}r$

Ratio of their radii of gyration=$\sqrt{\frac{3}{7}}$