Class 11 Exam > Class 11 Questions > What is the moment of inertia of a solid sphe...
Start Learning for Free
What is the moment of inertia of a solid sphere about its diameter?
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
What is the moment of inertia of a solid sphere about its diameter?a)b...
We have to consider solid sphere contribution of infinite small solid cylinder.
Icylinder = ½ MR²
dI = ½ dmr²
dm = pdV
dV = πr²dx
By substituting dV into dm
dm = pπr²dx
Now dm into dI
dI = ½ r²pπr²dx = ½ pπr⁴dx
Now, r² = R²-x²
dI = ½ pπ(R²-x²)²dx
Integrate both sides
I = ½ pπ 16/15 R²
P = M/V
P = M/4/3πR³ (density of sphere)
After substituting
I = 2/5MR2
Icylinder = ½ MR²
dI = ½ dmr²
dm = pdV
dV = πr²dx
By substituting dV into dm
dm = pπr²dx
Now dm into dI
dI = ½ r²pπr²dx = ½ pπr⁴dx
Now, r² = R²-x²
dI = ½ pπ(R²-x²)²dx
Integrate both sides
I = ½ pπ 16/15 R²
P = M/V
P = M/4/3πR³ (density of sphere)
After substituting
I = 2/5MR2
Most Upvoted Answer
What is the moment of inertia of a solid sphere about its diameter?a)b...
We have to consider solid sphere contribution of infinite small solid cylinder .
I(cylinder)=1/2MR²
dI=1/2dmr²
dm= pdV
dV=πr²dx
By substituting dV into dm
dm=pπr²dx
now dm into dI
dI=1/2r²pπr²dx=1/2pπr⁴dx
from figure ,
r²=R²-x²
dI=1/2pπ(R²-x²)²dx
integrate both sides_
I=1/2pπ16/15R²
p=M/V
p=M/4/3πR³(density of sphere)
substitute
I=2/5MR²
I(cylinder)=1/2MR²
dI=1/2dmr²
dm= pdV
dV=πr²dx
By substituting dV into dm
dm=pπr²dx
now dm into dI
dI=1/2r²pπr²dx=1/2pπr⁴dx
from figure ,
r²=R²-x²
dI=1/2pπ(R²-x²)²dx
integrate both sides_
I=1/2pπ16/15R²
p=M/V
p=M/4/3πR³(density of sphere)
substitute
I=2/5MR²
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
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?
Question Description
What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct 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 What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct 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 What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?.
What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct 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 What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct 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 What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?.
Solutions for What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct 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 What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the moment of inertia of a solid sphere about its diameter?a)b)c)d)Correct 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