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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?
Most Upvoted Answer
Two magnets are held together in a vibration magnetometer and are allo...
Analysis:

Given Data:
- Number of oscillations per minute with like poles together = 12
- Number of oscillations per minute with unlike poles together = 4

Concept:
The time period of oscillation in a vibration magnetometer is given by:
T = 2π√(I/mB)
where T is the time period, I is the moment of inertia of the system, m is the magnetic moment of the magnet, and B is the magnetic field strength.

Calculation:
- Let the magnetic moments of the two magnets be M1 and M2.
- For like poles together, the time period T1 is inversely proportional to the magnetic moment. Hence, T1 ∝ 1/M1
- For unlike poles together, the time period T2 is also inversely proportional to the magnetic moment. Hence, T2 ∝ 1/M2
Given that the number of oscillations per minute is inversely proportional to the time period, we have:
- For like poles together, T1 ∝ 1/M1 => 12 ∝ 1/M1
- For unlike poles together, T2 ∝ 1/M2 => 4 ∝ 1/M2
Therefore, the ratio of magnetic moments M1/M2 = 4/12 = 1/3 = 5/4
Therefore, the correct answer is option '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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