For a thin flat circular disc, the radius of gyration about a diameter as axis is k. if the disk is cut along a diameter AB as shown in to two equal pieces, then find the radius of gyration of each piece about AB.

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Detailed Solution

For circular disc, $k = \sqrt{\frac{I}{m}}$
This disc cut into two equal pieces about AB, when each Mass $M^{1} = \frac{M}{2} and I^{1} = \frac{I}{2}$
$∴$ Radius of gyration of each piece is $K^{1} = \sqrt{\frac{I^{1}}{M^{1}}} = \sqrt{\frac{I / 2}{M / 2}} = \sqrt{\frac{I}{M}} = k$

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