The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is [2022]

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Solution

Q.
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is [2022]

1 $2 : 1$

2 $\sqrt{2} : 1$

3 $4 : 1$

4 $1 : \sqrt{2}$

Ans.
(2)

The radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane is,

$k = \frac{R}{\sqrt{2}}$ ...(i)

Radius of gyration of disc about its diameter is $k' = \frac{R}{2}$ ...(ii)

Then, $\frac{k}{k'} = \frac{\frac{R}{\sqrt{2}}}{\frac{R}{2}} = \sqrt{2} : 1$

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