The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of a thin hollow sphere of same - Physics MCQ NEET 2023 2026 | ExamTest.live | ExamTest.live

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The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of a thin hollow sphere of same mass and radius about its axis is:

A $3 : 5$
B $3 : 5$
C $2 : 5$
D $2 : 5$

Solution & Step-by-step Explanation

Radius of gyration k is given by I = M k^{2} ⟹ k = I / M .Solid Sphere: I_{1} = \frac{2}{5} M R^{2} ⟹ k_{1} = \frac{2}{5} R Hollow Sphere: I_{2} = \frac{2}{3} M R^{2} ⟹ k_{2} = \frac{2}{3} R Ratio: \frac{k _{1}}{k _{2}} = \frac{2/5}{2/3} = \frac{3}{5} = \frac{3}{5} The ratio is 3 : 5 .

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The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of a thin hollow sphere of same mass and radius about its axis is:

A

3 : 5

B

3 : 5

C

2 : 5

D

2 : 5

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rotational mechanics radius of gyration

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