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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 the thin hollow sphere of same mass and radius about its axis is :-
- a)5 : 3
- b)2 : 5
- c)√5 : √3
- d)√3 : √5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The ratio of radius of gyration of a solid sphere of massMand radiusRa...
To solve this problem, we need to find the ratio of the radius of gyration for a solid sphere (K₁) to the radius of gyration for a thin hollow sphere (K₂) of the same mass M and radius R.
The moment of inertia (I) of a solid sphere about its own axis is given by :
The radius of gyration (K) is related to the moment of inertia (I) and mass (M) by the formula :
I = Mk2
So for the solid sphere, we can find K₁ using :
Now, for a thin hollow sphere, the moment of inertia about its axis is given by :
We can find K₂ using :
Now, we need to find the ratio K₁ : K₂ :
The R terms cancel out, and we are left with :
Simplify by taking the square root of the fraction :
Now, the square root of 2 terms cancel out, giving us :
Most Upvoted Answer
The ratio of radius of gyration of a solid sphere of massMand radiusRa...
To find the ratio of the radius of gyration of the solid sphere to the thin hollow sphere, we need to find the formula for the radius of gyration for each.
The formula for the radius of gyration of a solid sphere is:
\[k_{\text{solid}} = \sqrt{\frac{2}{5}R^2}\]
The formula for the radius of gyration of a thin hollow sphere is:
\[k_{\text{hollow}} = \sqrt{\frac{2}{3}R^2}\]
To find the ratio, we can divide the two formulas:
\[\frac{k_{\text{solid}}}{k_{\text{hollow}}} = \frac{\sqrt{\frac{2}{5}R^2}}{\sqrt{\frac{2}{3}R^2}}\]
Simplifying, we get:
\[\frac{k_{\text{solid}}}{k_{\text{hollow}}} = \sqrt{\frac{3}{5}}\]
Therefore, the ratio of the radius of gyration of the solid sphere to the thin hollow sphere is:
\[\boxed{\text{(b) 2 : 5}}\]
The formula for the radius of gyration of a solid sphere is:
\[k_{\text{solid}} = \sqrt{\frac{2}{5}R^2}\]
The formula for the radius of gyration of a thin hollow sphere is:
\[k_{\text{hollow}} = \sqrt{\frac{2}{3}R^2}\]
To find the ratio, we can divide the two formulas:
\[\frac{k_{\text{solid}}}{k_{\text{hollow}}} = \frac{\sqrt{\frac{2}{5}R^2}}{\sqrt{\frac{2}{3}R^2}}\]
Simplifying, we get:
\[\frac{k_{\text{solid}}}{k_{\text{hollow}}} = \sqrt{\frac{3}{5}}\]
Therefore, the ratio of the radius of gyration of the solid sphere to the thin hollow sphere is:
\[\boxed{\text{(b) 2 : 5}}\]
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The ratio of radius of gyration of a solid sphere of massMand radiusRabout its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-a)5 : 3b)2 : 5c)√5 : √3d)√3 : √5Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The ratio of radius of gyration of a solid sphere of massMand radiusRabout its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-a)5 : 3b)2 : 5c)√5 : √3d)√3 : √5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of radius of gyration of a solid sphere of massMand radiusRabout its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-a)5 : 3b)2 : 5c)√5 : √3d)√3 : √5Correct answer is option 'D'. Can you explain this answer?.
The ratio of radius of gyration of a solid sphere of massMand radiusRabout its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-a)5 : 3b)2 : 5c)√5 : √3d)√3 : √5Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The ratio of radius of gyration of a solid sphere of massMand radiusRabout its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-a)5 : 3b)2 : 5c)√5 : √3d)√3 : √5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of radius of gyration of a solid sphere of massMand radiusRabout its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-a)5 : 3b)2 : 5c)√5 : √3d)√3 : √5Correct answer is option 'D'. Can you explain this answer?.
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