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One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________
- a)IA=IB
- b)IA is greater thab IB
- c)IA is lesser than IB
- d)IA/IB =ρA/ρB
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
One solid sphere ‘A’ and another hollow sphere ‘B&rs...
Introduction
In this discussion, we analyze the moments of inertia of a solid sphere ‘A’ and a hollow sphere ‘B’, both having the same mass and outer radius.
Moments of Inertia
- The moment of inertia (I) is a measure of an object's resistance to rotational motion about an axis.
- For a solid sphere:
- IA = (2/5) * m * R^2
- Here, m is the mass and R is the radius of the solid sphere.
- For a hollow sphere:
- IB = (2/3) * m * R^2
- This formula applies to a thin-walled hollow sphere.
Comparison of IA and IB
- To compare IA and IB, we can substitute the formulas derived:
- IA = (2/5) * m * R^2
- IB = (2/3) * m * R^2
- When comparing these, we see:
- (2/5) < (2/3)="" />
Conclusion
- Therefore, it follows that:
- IA < />
- This indicates that the moment of inertia of the solid sphere is less than that of the hollow sphere.
Final Answer
- The correct answer is option 'C': IA is lesser than IB.
This conclusion arises from the fundamental differences in mass distribution between a solid sphere and a hollow sphere, leading to different resistances to rotational motion.
In this discussion, we analyze the moments of inertia of a solid sphere ‘A’ and a hollow sphere ‘B’, both having the same mass and outer radius.
Moments of Inertia
- The moment of inertia (I) is a measure of an object's resistance to rotational motion about an axis.
- For a solid sphere:
- IA = (2/5) * m * R^2
- Here, m is the mass and R is the radius of the solid sphere.
- For a hollow sphere:
- IB = (2/3) * m * R^2
- This formula applies to a thin-walled hollow sphere.
Comparison of IA and IB
- To compare IA and IB, we can substitute the formulas derived:
- IA = (2/5) * m * R^2
- IB = (2/3) * m * R^2
- When comparing these, we see:
- (2/5) < (2/3)="" />
Conclusion
- Therefore, it follows that:
- IA < />
- This indicates that the moment of inertia of the solid sphere is less than that of the hollow sphere.
Final Answer
- The correct answer is option 'C': IA is lesser than IB.
This conclusion arises from the fundamental differences in mass distribution between a solid sphere and a hollow sphere, leading to different resistances to rotational motion.
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Community Answer
One solid sphere ‘A’ and another hollow sphere ‘B&rs...
In a hollow sphere, the mass is distributed away from the axis of rotation. So, its moment of inertia is greater than that of a solid sphere.
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One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer?.
One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer?.
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One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that _____________a)IA=IBb)IA is greater thab IBc)IA is lesser than IBd)IA/IB =ρA/ρBCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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