The radius of gyration \(K\) of a hollow sphere of mass \(M\) and radius \(R\) about a certain axis is equal…

1. \(R / \sqrt{2}\)
2. \(R / \sqrt{3}\)
3. \(R / \sqrt{7}\)
4. \(R / \sqrt{5}\)

Solution

Let \(x\) be the distance of the axis from the centre of the sphere [Fig.]. From parallel axes theorem
\(\begin{aligned}
& I_{X Y} &=I_{A B}+M x^{2} \\
\Rightarrow & M K^{2} &=\frac{2}{3} M R^{2}+M x^{2}
\end{aligned}\)
Given
\(\begin{array}{l}
K=R \text {. Hence } \\
R^{2}=\frac{2}{3} R^{2}+x^{2} \Rightarrow x=\frac{R}{\sqrt{3}}
\end{array}\)

Asked in: JEE Mains - Rotational Motion - Test 2

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