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A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained with
- a)iron and aluminium layers in alternate order
- b)aluminium at interior and iron surrounding it
- c)iron at interior and almuminium surrouning it
- d)either '1' or '3'
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A circular disc is to be made by using iron aluminium, so that it acqu...
Understanding Moment of Inertia
The moment of inertia (I) of a body is a measure of how difficult it is to change its rotational motion about an axis. For a disc, the distribution of mass relative to the axis of rotation is crucial in determining its moment of inertia.
Material Properties
- Iron has a higher density (approximately 7.87 g/cm³) compared to aluminium (approximately 2.70 g/cm³).
- The moment of inertia is influenced by both the mass and the distance from the axis of rotation.
Configuration for Maximum Moment of Inertia
To achieve the maximum moment of inertia for a circular disc, the mass must be distributed as far from the axis as possible.
- Option A: Iron and aluminium layers in alternate order.
- This configuration does not maximize the distance of the heavier mass (iron) from the axis, as alternating layers would place lighter aluminium close to the axis.
- Option B: Aluminium at the interior and iron surrounding it.
- This arrangement allows the denser iron to be situated further from the axis, significantly increasing the moment of inertia. The lighter aluminium core minimizes the inertia contribution from the center.
- Option C: Iron at the interior and aluminium surrounding it.
- Here, the heavier iron is close to the axis, reducing its contribution to the moment of inertia compared to having it on the outside.
- Option D: Either 1 or 3.
- This is incorrect as neither option maximizes the moment of inertia effectively.
Conclusion
Thus, the correct configuration for maximizing the moment of inertia of the disc is Option B: aluminium at the interior and iron surrounding it. This setup maximizes the mass further from the axis, enhancing the moment of inertia.
The moment of inertia (I) of a body is a measure of how difficult it is to change its rotational motion about an axis. For a disc, the distribution of mass relative to the axis of rotation is crucial in determining its moment of inertia.
Material Properties
- Iron has a higher density (approximately 7.87 g/cm³) compared to aluminium (approximately 2.70 g/cm³).
- The moment of inertia is influenced by both the mass and the distance from the axis of rotation.
Configuration for Maximum Moment of Inertia
To achieve the maximum moment of inertia for a circular disc, the mass must be distributed as far from the axis as possible.
- Option A: Iron and aluminium layers in alternate order.
- This configuration does not maximize the distance of the heavier mass (iron) from the axis, as alternating layers would place lighter aluminium close to the axis.
- Option B: Aluminium at the interior and iron surrounding it.
- This arrangement allows the denser iron to be situated further from the axis, significantly increasing the moment of inertia. The lighter aluminium core minimizes the inertia contribution from the center.
- Option C: Iron at the interior and aluminium surrounding it.
- Here, the heavier iron is close to the axis, reducing its contribution to the moment of inertia compared to having it on the outside.
- Option D: Either 1 or 3.
- This is incorrect as neither option maximizes the moment of inertia effectively.
Conclusion
Thus, the correct configuration for maximizing the moment of inertia of the disc is Option B: aluminium at the interior and iron surrounding it. This setup maximizes the mass further from the axis, enhancing the moment of inertia.
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A circular disc is to be made by using iron aluminium, so that it acqu...
Understanding Moment of Inertia
The moment of inertia (I) quantifies how much resistance a body offers to rotational motion about an axis. For a circular disc, the distribution of mass relative to the axis of rotation significantly influences its moment of inertia.
Composition of the Disc
When constructing a circular disc from two materials, the positioning of these materials affects the overall moment of inertia.
Material Properties
- Iron: Higher density and mass compared to aluminium.
- Aluminium: Lower density and mass, but provides a lighter structure.
Maximizing Moment of Inertia
To maximize the moment of inertia, it is essential to have more mass distributed further from the axis of rotation. This is because the moment of inertia is greater for mass located at larger distances from the center.
Analysis of Options
- Option A: Iron and aluminium layers in alternate order.
- This arrangement does not optimize the distance of mass from the axis effectively.
- Option B: Aluminium at the interior and iron surrounding it.
- The iron, being denser, is placed at a greater radius from the axis, which increases the moment of inertia significantly.
- Option C: Iron at the interior and aluminium surrounding it.
- This configuration places less mass further from the axis, reducing the moment of inertia.
- Option D: Either option A or C.
- This is incorrect since neither option A nor option C maximizes the moment of inertia.
Conclusion
Thus, option B is correct: placing aluminium in the center and iron surrounding it maximizes the moment of inertia by leveraging the greater density of iron at a larger radius from the axis. This configuration effectively increases rotational resistance, making it the optimal choice.
The moment of inertia (I) quantifies how much resistance a body offers to rotational motion about an axis. For a circular disc, the distribution of mass relative to the axis of rotation significantly influences its moment of inertia.
Composition of the Disc
When constructing a circular disc from two materials, the positioning of these materials affects the overall moment of inertia.
Material Properties
- Iron: Higher density and mass compared to aluminium.
- Aluminium: Lower density and mass, but provides a lighter structure.
Maximizing Moment of Inertia
To maximize the moment of inertia, it is essential to have more mass distributed further from the axis of rotation. This is because the moment of inertia is greater for mass located at larger distances from the center.
Analysis of Options
- Option A: Iron and aluminium layers in alternate order.
- This arrangement does not optimize the distance of mass from the axis effectively.
- Option B: Aluminium at the interior and iron surrounding it.
- The iron, being denser, is placed at a greater radius from the axis, which increases the moment of inertia significantly.
- Option C: Iron at the interior and aluminium surrounding it.
- This configuration places less mass further from the axis, reducing the moment of inertia.
- Option D: Either option A or C.
- This is incorrect since neither option A nor option C maximizes the moment of inertia.
Conclusion
Thus, option B is correct: placing aluminium in the center and iron surrounding it maximizes the moment of inertia by leveraging the greater density of iron at a larger radius from the axis. This configuration effectively increases rotational resistance, making it the optimal choice.
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A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer?.
A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer?.
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A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A circular disc is to be made by using iron aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It can be obtained witha)iron and aluminium layers in alternate orderb)aluminium at interior and iron surrounding itc)iron at interior and almuminium surrouning itd)either 1 or 3Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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