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A disc of metal is melted to recast in the form of a solid sphere. The moment of inertias about a vertical axis passing through the centre would -
- a)decrease
- b)increase
- c)remains same
- d)nothing can be said
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A disc of metal is melted to recast in the form of a solid sphere. The...
Moment of inertia will decrease, because
Id=1/2mr2 and Is=2/5mr2,
the radius of sphere formed on recasting the disc will also decrease.
Id=1/2mr2 and Is=2/5mr2,
the radius of sphere formed on recasting the disc will also decrease.
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A disc of metal is melted to recast in the form of a solid sphere. The...
Moment of Inertia:
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. For a solid sphere, the moment of inertia can be calculated using the formula:
I = (2/5) * m * r^2
Where I is the moment of inertia, m is the mass of the sphere, and r is the radius of the sphere.
Moment of Inertia of a Disc:
The moment of inertia of a disc can be calculated using the formula:
I = (1/4) * m * r^2
Where I is the moment of inertia, m is the mass of the disc, and r is the radius of the disc.
Conversion of Disc to Sphere:
When the disc is melted and recast into the form of a solid sphere, the mass remains the same. However, the mass distribution changes as the disc is transformed into a sphere.
Effect on Moment of Inertia:
The moment of inertia of a sphere is given by the formula:
I = (2/5) * m * r^2
Comparing this with the moment of inertia of the disc, we can see that the moment of inertia of the sphere is greater.
Therefore, by recasting the disc into a solid sphere, the moment of inertia about a vertical axis passing through the center increases.
Explanation:
When the disc is melted and recast into a solid sphere, the mass remains the same. However, the distribution of mass changes. In the case of a disc, the mass is concentrated towards the outer edge, resulting in a smaller moment of inertia. On the other hand, in the case of a sphere, the mass is distributed more evenly, resulting in a larger moment of inertia.
So, by recasting the disc into a solid sphere, the moment of inertia about a vertical axis passing through the center increases.
Conclusion:
The moment of inertia about a vertical axis passing through the center would increase when a disc of metal is melted and recast in the form of a solid sphere.
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. For a solid sphere, the moment of inertia can be calculated using the formula:
I = (2/5) * m * r^2
Where I is the moment of inertia, m is the mass of the sphere, and r is the radius of the sphere.
Moment of Inertia of a Disc:
The moment of inertia of a disc can be calculated using the formula:
I = (1/4) * m * r^2
Where I is the moment of inertia, m is the mass of the disc, and r is the radius of the disc.
Conversion of Disc to Sphere:
When the disc is melted and recast into the form of a solid sphere, the mass remains the same. However, the mass distribution changes as the disc is transformed into a sphere.
Effect on Moment of Inertia:
The moment of inertia of a sphere is given by the formula:
I = (2/5) * m * r^2
Comparing this with the moment of inertia of the disc, we can see that the moment of inertia of the sphere is greater.
Therefore, by recasting the disc into a solid sphere, the moment of inertia about a vertical axis passing through the center increases.
Explanation:
When the disc is melted and recast into a solid sphere, the mass remains the same. However, the distribution of mass changes. In the case of a disc, the mass is concentrated towards the outer edge, resulting in a smaller moment of inertia. On the other hand, in the case of a sphere, the mass is distributed more evenly, resulting in a larger moment of inertia.
So, by recasting the disc into a solid sphere, the moment of inertia about a vertical axis passing through the center increases.
Conclusion:
The moment of inertia about a vertical axis passing through the center would increase when a disc of metal is melted and recast in the form of a solid sphere.
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A disc of metal is melted to recast in the form of a solid sphere. The moment of inertias about a vertical axis passing through the centre would -a)decreaseb)increasec)remains samed)nothing can be saidCorrect answer is option 'A'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A disc of metal is melted to recast in the form of a solid sphere. The moment of inertias about a vertical axis passing through the centre would -a)decreaseb)increasec)remains samed)nothing can be saidCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc of metal is melted to recast in the form of a solid sphere. The moment of inertias about a vertical axis passing through the centre would -a)decreaseb)increasec)remains samed)nothing can be saidCorrect answer is option 'A'. Can you explain this answer?.
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