NEET 2022, Physics Q7: Moment of Inertia

NEET2022Physics

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 :

A
$2 : 1$
B
$4 : 1$
C
$1 : 2$
D
$2 : 1$

Solution

Moment of inertia of a thin uniform disc about its central axis (perpendicular to the plane): $I_{1} = \frac{m R ^{2}}{2}$ .

About a diameter: $I_{2} = \frac{m R ^{2}}{4}$ .

Radius of gyration $k = I / m$ , so $\frac{k _{1}}{k _{2}} = \frac{I _{1}}{I _{2}} = \frac{m R ^{2} /2}{m R ^{2} /4} = 2$ .

Hence the ratio is $2 : 1$ .

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NEET 2022, Physics Q7: Moment of Inertia

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