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Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?
- a)2/5 kg
- b)5 kg
- c)3 kg
- d)2/3 kg
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Moment of inertia of two spheres of equal radii are equal. One of the ...
We know that for a solid sphere of mass S and radius r, moment of inertia I = ⅖ Sr2
Similarly for a hollow sphere of mass H and radius r, moment of inertia I = ⅔ Hr2
Thus if there radii and I are equal the ratio of there mass can be find by equating both as
I = ⅖ Sr2 = ⅔ Hr2
Hence we het H/S = ⅗
So if S is 5kg we get H = 3kg
Similarly for a hollow sphere of mass H and radius r, moment of inertia I = ⅔ Hr2
Thus if there radii and I are equal the ratio of there mass can be find by equating both as
I = ⅖ Sr2 = ⅔ Hr2
Hence we het H/S = ⅗
So if S is 5kg we get H = 3kg
Most Upvoted Answer
Moment of inertia of two spheres of equal radii are equal. One of the ...
Given:
Moment of inertia of two spheres of equal radii are equal.
Mass of solid sphere, m1 = 5 kg
To find:
Mass of hollow sphere, m2
Concept:
Moment of inertia is the resistance of a body against the change in its rotational motion. It depends on the mass and distribution of mass of the body.
Formula:
Moment of inertia of a solid sphere of radius r and mass m is given by
I = 2/5mr²
Moment of inertia of a hollow sphere of radius r, mass m and thickness t is given by
I = 2/3m(r²+t²)
Calculation:
Let the mass of hollow sphere be m2 and radius be r
Given, moment of inertia of both spheres are equal
∴ 2/5 m1r² = 2/3 m2(r²+t²)
Here, r is common for both spheres, so we can cancel it out.
2/5 m1 = 2/3 m2(1 + (t/r)²)
Since the hollow sphere is larger in size than solid sphere, t/r > 0
So, 1 + (t/r)² > 1
∴ 2/5 m1 < 2/3="" />
Substituting m1 = 5 kg, we get
2/5 * 5 < 2/3="" />
2 < 2/3="" />
m2 > 3 kg
Thus, the mass of the hollow sphere is greater than 3 kg.
Option (c) 3 kg is the correct answer.
Moment of inertia of two spheres of equal radii are equal.
Mass of solid sphere, m1 = 5 kg
To find:
Mass of hollow sphere, m2
Concept:
Moment of inertia is the resistance of a body against the change in its rotational motion. It depends on the mass and distribution of mass of the body.
Formula:
Moment of inertia of a solid sphere of radius r and mass m is given by
I = 2/5mr²
Moment of inertia of a hollow sphere of radius r, mass m and thickness t is given by
I = 2/3m(r²+t²)
Calculation:
Let the mass of hollow sphere be m2 and radius be r
Given, moment of inertia of both spheres are equal
∴ 2/5 m1r² = 2/3 m2(r²+t²)
Here, r is common for both spheres, so we can cancel it out.
2/5 m1 = 2/3 m2(1 + (t/r)²)
Since the hollow sphere is larger in size than solid sphere, t/r > 0
So, 1 + (t/r)² > 1
∴ 2/5 m1 < 2/3="" />
Substituting m1 = 5 kg, we get
2/5 * 5 < 2/3="" />
2 < 2/3="" />
m2 > 3 kg
Thus, the mass of the hollow sphere is greater than 3 kg.
Option (c) 3 kg is the correct answer.
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Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer?
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Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer?.
Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer?.
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Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?a)2/5 kgb)5 kgc)3 kgd)2/3kgCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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