Class 11 Exam > Class 11 Questions > Moment of inertia of two spheres of equal rad...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
Free Test
FREE
| Start Free Test |
Community Answer
Moment of inertia of two spheres of equal radii are equal. One of the ...
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Top Courses for Class 11View all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning 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? defined & explained in the simplest way possible. Besides giving the explanation 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?, 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
ample number of questions to practice 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? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup