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Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio of
- a)4:5
- b)5:4
- c)144:225
- d)225:144
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two similar bar magnets of the same mass and dimensions freely suspend...
Concept:
The time period of oscillation of a bar magnet in a magnetic field is given by:
\[T = 2\pi\sqrt{\frac{I}{M B}}\]
where,
T = time period of oscillation,
I = moment of inertia of the magnet,
M = magnetic moment of the magnet,
B = magnetic field strength.
Given:
Number of oscillations for first magnet = 12 per minute = 12/60 = 0.2 Hz
Number of oscillations for second magnet = 15 per minute = 15/60 = 0.25 Hz
Calculation:
Let the magnetic moments of the two magnets be \(M_1\) and \(M_2\).
For the first magnet:
\[T_1 = \frac{1}{0.2} = 5s\]
\[M_1 = \frac{4\pi^2 I}{T_1^2 B}\]
For the second magnet:
\[T_2 = \frac{1}{0.25} = 4s\]
\[M_2 = \frac{4\pi^2 I}{T_2^2 B}\]
Now, the ratio of magnetic moments:
\[\frac{M_1}{M_2} = \frac{T_2^2}{T_1^2} = \frac{16}{25} = \frac{144}{225}\]
Therefore, the magnetic moments are in the ratio 144:225, which corresponds to option (c).
The time period of oscillation of a bar magnet in a magnetic field is given by:
\[T = 2\pi\sqrt{\frac{I}{M B}}\]
where,
T = time period of oscillation,
I = moment of inertia of the magnet,
M = magnetic moment of the magnet,
B = magnetic field strength.
Given:
Number of oscillations for first magnet = 12 per minute = 12/60 = 0.2 Hz
Number of oscillations for second magnet = 15 per minute = 15/60 = 0.25 Hz
Calculation:
Let the magnetic moments of the two magnets be \(M_1\) and \(M_2\).
For the first magnet:
\[T_1 = \frac{1}{0.2} = 5s\]
\[M_1 = \frac{4\pi^2 I}{T_1^2 B}\]
For the second magnet:
\[T_2 = \frac{1}{0.25} = 4s\]
\[M_2 = \frac{4\pi^2 I}{T_2^2 B}\]
Now, the ratio of magnetic moments:
\[\frac{M_1}{M_2} = \frac{T_2^2}{T_1^2} = \frac{16}{25} = \frac{144}{225}\]
Therefore, the magnetic moments are in the ratio 144:225, which corresponds to option (c).
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Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer?
Question Description
Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. 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 Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer?.
Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. 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 Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer?.
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Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Two similar bar magnets of the same mass and dimensions freely suspended by threads in a horizontal plane are found to make 12 oscillations and 15 oscillations per minute. Then their magnetic moments are in the ratio ofa)4:5b)5:4c)144:225d)225:144Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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