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Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together. 12 oscillations per minute are made, but for unlike poles together only 4 oscillations per minute are executed. The ratio of their magnetic moments is
- a)3:1
- b)1:3
- c)3:5
- d)5:4
Correct answer is option 'D'. Can you explain this answer?
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Explanation:
A vibration magnetometer is an instrument used to measure the magnetic moment of a magnet. In this instrument, two magnets are suspended by a thin fiber and allowed to oscillate in the earth's magnetic field.
When like poles of the magnets are together, they experience a repulsive force and oscillate faster than when unlike poles are together, which experience an attractive force and oscillate slower. Therefore, by measuring the oscillation frequency, we can determine the magnetic moment of the magnets.
Let the magnetic moments of the two magnets be M1 and M2. We can use the formula for the period of oscillation of a magnet in the earth's magnetic field:
T = 2π√(I/mB)
where T is the period of oscillation, I is the moment of inertia of the magnet, m is its magnetic moment, and B is the earth's magnetic field.
For like poles together, we have:
T1 = 2π√(I/m1B) = 1/2 f1
where f1 is the frequency of oscillation (12 oscillations per minute).
For unlike poles together, we have:
T2 = 2π√(I/m2B) = 1/4 f2
where f2 is the frequency of oscillation (4 oscillations per minute).
Dividing the two equations, we get:
T1/T2 = (m2/m1)√(m1/m2) = 2
Squaring both sides, we get:
(m2/m1) * (m1/m2) = 4/1
or
m2/m1 = 2
Therefore, the ratio of the magnetic moments is 5:4 (since 2:1 is equivalent to 5:4).
Answer: d) 5:4
A vibration magnetometer is an instrument used to measure the magnetic moment of a magnet. In this instrument, two magnets are suspended by a thin fiber and allowed to oscillate in the earth's magnetic field.
When like poles of the magnets are together, they experience a repulsive force and oscillate faster than when unlike poles are together, which experience an attractive force and oscillate slower. Therefore, by measuring the oscillation frequency, we can determine the magnetic moment of the magnets.
Let the magnetic moments of the two magnets be M1 and M2. We can use the formula for the period of oscillation of a magnet in the earth's magnetic field:
T = 2π√(I/mB)
where T is the period of oscillation, I is the moment of inertia of the magnet, m is its magnetic moment, and B is the earth's magnetic field.
For like poles together, we have:
T1 = 2π√(I/m1B) = 1/2 f1
where f1 is the frequency of oscillation (12 oscillations per minute).
For unlike poles together, we have:
T2 = 2π√(I/m2B) = 1/4 f2
where f2 is the frequency of oscillation (4 oscillations per minute).
Dividing the two equations, we get:
T1/T2 = (m2/m1)√(m1/m2) = 2
Squaring both sides, we get:
(m2/m1) * (m1/m2) = 4/1
or
m2/m1 = 2
Therefore, the ratio of the magnetic moments is 5:4 (since 2:1 is equivalent to 5:4).
Answer: d) 5:4
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Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together. 12 oscillations per minute are made, but for unlike poles together only 4 oscillations per minute are executed. The ratio of their magnetic moments isa)3:1b)1:3c)3:5d)5:4Correct answer is option 'D'. Can you explain this answer?
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Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together. 12 oscillations per minute are made, but for unlike poles together only 4 oscillations per minute are executed. The ratio of their magnetic moments isa)3:1b)1:3c)3:5d)5:4Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together. 12 oscillations per minute are made, but for unlike poles together only 4 oscillations per minute are executed. The ratio of their magnetic moments isa)3:1b)1:3c)3:5d)5:4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together. 12 oscillations per minute are made, but for unlike poles together only 4 oscillations per minute are executed. The ratio of their magnetic moments isa)3:1b)1:3c)3:5d)5:4Correct answer is option 'D'. Can you explain this answer?.
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