JEE Exam > JEE Questions > From a uniform wire, two circular loops are m...
Start Learning for Free
From a uniform wire, two circular loops are made i) P of radius 'r' and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of 'n' is (diameter of the wire is very much smaller than r or nr)
- a)8
- b)6
- c)4
- d)2
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
From a uniform wire, two circular loops are made i) P of radius r and ...
Given: Two circular loops of radius r and nr are made from a uniform wire. The moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis.
To find: The value of n.
Solution:
Let the moment of inertia of P about its axis passing through its centre and perpendicular to its plane be I. Then, the moment of inertia of Q about its axis passing through its centre and perpendicular to its plane will be:
IQ = mr² + mr² + mr² + ...... n times
= mn(r/n)²
= m(r²/n)
Given, IQ = 8I
So, m(r²/n) = 8I
or, m(r/n)² = 8I/m
or, (r/n)² = 8I/m * 1/m
or, (r/n)² = 8I/m²
We know that the diameter of the wire is very much smaller than r or nr. So, we can assume that the wire is thin and we can use the formula for moment of inertia of a thin circular ring:
I = mR²
where m is the mass of the ring and R is the radius of the ring.
For the loop P, mass = M and radius = r.
So, IP = M*r²
For the loop Q, mass = M and radius = nr.
So, IQ = M*(nr)²
Given, IQ = 8IP
or, M*(nr)² = 8M*r²
or, (nr)² = 8r²
or, n² = 8
Therefore, n = 2 (since n cannot be negative).
Answer: The value of n is 2.
To find: The value of n.
Solution:
Let the moment of inertia of P about its axis passing through its centre and perpendicular to its plane be I. Then, the moment of inertia of Q about its axis passing through its centre and perpendicular to its plane will be:
IQ = mr² + mr² + mr² + ...... n times
= mn(r/n)²
= m(r²/n)
Given, IQ = 8I
So, m(r²/n) = 8I
or, m(r/n)² = 8I/m
or, (r/n)² = 8I/m * 1/m
or, (r/n)² = 8I/m²
We know that the diameter of the wire is very much smaller than r or nr. So, we can assume that the wire is thin and we can use the formula for moment of inertia of a thin circular ring:
I = mR²
where m is the mass of the ring and R is the radius of the ring.
For the loop P, mass = M and radius = r.
So, IP = M*r²
For the loop Q, mass = M and radius = nr.
So, IQ = M*(nr)²
Given, IQ = 8IP
or, M*(nr)² = 8M*r²
or, (nr)² = 8r²
or, n² = 8
Therefore, n = 2 (since n cannot be negative).
Answer: The value of n is 2.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer?
Question Description
From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer?.
From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer?.
Solutions for From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice From a uniform wire, two circular loops are made i) P of radius r and ii)Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)a)8b)6c)4d)2Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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