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 - Physics MCQ NEET 2022 2026 | ExamTest.live | ExamTest.live

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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 $2 : 1$
C $4 : 1$
D $1 : 2$

Solution & Step-by-step Explanation

Radius of gyration k is defined by I = M k^{2} .About an axis through the center and normal to the plane: I_{1} = \frac{1}{2} M R^{2} ⟹ k_{1}^{2} = \frac{R ^{2}}{2} ⟹ k_{1} = \frac{R}{2} About its diameter: I_{2} = \frac{1}{4} M R^{2} ⟹ k_{2}^{2} = \frac{R ^{2}}{4} ⟹ k_{2} = \frac{R}{2} Ratio \frac{k _{1}}{k _{2}} = \frac{R / 2}{R /2} = \frac{2}{2} = \frac{2}{1} .Thus, the ratio is 2 : 1 .

Practice this question

Try it yourself before checking the explanation above.

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

2 : 1

C

4 : 1

D

1 : 2

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rotational mechanics radius of gyration

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