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The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is
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Verified Answer
The correct answer is:
$1: \sqrt{2}$
$$
\begin{aligned}
& \frac{l_{\text {diso }}}{l_{\text {ring }}}=\frac{M R^2 / 2}{M R^2}=\frac{M K_{\text {disc }}^2}{M K_{\text {ring }}^2} \\
& \Rightarrow \frac{K_{\text {dise }}}{K_{\text {ring }}}=\frac{1}{\sqrt{2}}
\end{aligned}
$$
\begin{aligned}
& \frac{l_{\text {diso }}}{l_{\text {ring }}}=\frac{M R^2 / 2}{M R^2}=\frac{M K_{\text {disc }}^2}{M K_{\text {ring }}^2} \\
& \Rightarrow \frac{K_{\text {dise }}}{K_{\text {ring }}}=\frac{1}{\sqrt{2}}
\end{aligned}
$$
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