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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?
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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.
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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?
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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?.
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