First slide

Moment of intertia

Question

If a disc of mass m and radius r is reshaped into a ring of radius 2r, the mass remaining the same, the radius of gyration about centroidal axis perpendicular to plane goes up by a factor of

Moderate

A

$\sqrt{2}$
B

2
C

2 $\sqrt{2}$
D

4

Solution

Radius of gyration of disc, $K_{D} = \sqrt{\frac{I_{D}}{m}} = \sqrt{\frac{\frac{1}{2} m r^{2}}{m}} = \frac{r}{\sqrt{2}}$
Radius of gyration of ring, $K_{R} = \sqrt{\frac{I_{R}}{m}} = \sqrt{\frac{m (2 r)^{2}}{m}} = 2 r$
$∴ \frac{K_{R}}{K_{D}} = 2 \sqrt{2}$

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