Question

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is \(\sqrt{\frac{8}{x}}\) . The value of x is:

(1) 34

(2) 17

(3) 67

(4) 51

Answer 1

Correct option is : (3) 67

Hollow Sphere \(\frac{2}{3} m R^2=\mathrm{mk}_1^2 \Rightarrow \mathrm{k}_1=\sqrt{\frac{2}{3}} \mathrm{R}\) 

Solid cylinder \(\frac{\mathrm{m}(\ 4 \mathrm{R})^2}{3}+\frac{\mathrm{mR}^2}{4}=\mathrm{mk}_2^2\)    

\(\mathrm{k}_2=\sqrt{\frac{67}{12}} \mathrm{R} \)

\(\frac{\mathrm{k}_1}{\mathrm{k}_2}=\sqrt{\frac{2}{3} \times \frac{12}{67}}=\sqrt{\frac{8}{67}}\) 

\(\Rightarrow \mathrm{x}=67\)