Question 132: Centre of Mass and Rotational Motion

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 $$A B$$ as shown in figure is $$\sqrt{8 / x}$$. The value of $$x$$ is :

Accepted Answer

For hollow sphere
$$\begin{aligned}
& I_1=\frac{2}{3} m R^2=\left(\sqrt{\frac{2}{3}} Right)^2 m \
& 	herefore \quad K_1=\sqrt{\frac{2}{3}} R
\end{aligned}$$
For solid cylinder
$$\begin{aligned}
& I_2=\frac{1}{4} m R^2+\frac{m}{3}(4 R)^2 \
& =\left(\sqrt{\frac{67}{12}} Right)^2 m \
& 	herefore \quad K_2=\sqrt{\frac{67}{12}} R \
& \Rightarrow \frac{K_1}{K_2}=\sqrt{\frac{2}{3} 	imes \frac{12}{67}} \
& =\sqrt{\frac{8}{67}}
\end{aligned}$$
$$\Rightarrow \quad x=67$$

Answer

34

Answer

51

Answer

67

Answer

17

Centre of Mass and Rotational Motion

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 $A B as shown in figure is \sqrt{8 / x}. The value of x$ is :

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