QJEEM24Phf71f: JEE Main 2024 Physics - Class 11 JEEM24Phf71f Solution: Ratio of radius of gyration of a hollow sphere to that of a…

For hollow sphere

$\begin{aligned}& I_1=\frac{2}{3} m R^2=\left(\sqrt{\frac{2}{3}} R\right)^2 m \\& \therefore \quad K_1=\sqrt{\frac{2}{3}} R\end{aligned}$

For solid cylinder

$\begin{aligned}& I_2=\frac{1}{4} m R^2+\frac{m}{3}(4 R)^2 \\& =\left(\sqrt{\frac{67}{12}} R\right)^2 m \\& \therefore \quad K_2=\sqrt{\frac{67}{12}} R \\& \Rightarrow \frac{K_1}{K_2}=\sqrt{\frac{2}{3} \times \frac{12}{67}} \\& =\sqrt{\frac{8}{67}}\end{aligned}$

$\Rightarrow \quad x=67$