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In a vibration magnetometer, the time-period of magnets when the identical poles are in the same directon is 3 s. When the polarity of weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets is
- a)9:16
- b)16:9
- c)7:25
- d)25:7
Correct answer is option 'D'. Can you explain this answer?
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In a vibration magnetometer, the time-period of magnets when the ident...
Vibration Magnetometer and Calculation of Magnetic Moment Ratio
Introduction:
In a vibration magnetometer, the time-period of magnets when the identical poles are in the same direction is 3 s. When the polarity of the weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets is to be calculated.
Formula Used:
The time-period of oscillation of a magnet in a vibration magnetometer is given by the formula:
T = 2π √(I/mB)
where T is the time-period of oscillation, I is the moment of inertia of the magnet, m is the magnetic moment of the magnet, and B is the magnetic field strength.
Solution:
Let the magnetic moment of the stronger magnet be m1 and that of the weaker magnet be m2.
The given time-period of oscillation when the identical poles are in the same direction is 3 s.
Hence, for the stronger magnet,
T1 = 2π √(I/m1B) = 3
Squaring both sides and simplifying, we get:
m1/T1^2 = I/4π^2B
When the polarity of the weaker magnet is reversed, the combination makes 15 oscillations per minute.
Hence, for the combination of magnets,
T2 = 60/15 = 4 s
The time-period of oscillation for the combination of magnets is given by:
T2 = 2π √(I/(m1 + m2)B)
Squaring both sides and simplifying, we get:
(m1 + m2)/(T2^2 - T1^2) = I/4π^2B
Substituting the values of T1 and T2, and simplifying the above two equations, we get:
m1/T1^2 = (m1 + m2)/(T2^2 - T1^2)
Solving for m2/m1, we get:
m2/m1 = (T2^2 - T1^2)/T1^2
Substituting the given values, we get:
m2/m1 = (16 - 9)/9 = 7/9
Hence, the ratio of magnetic moments of the magnets is 25:7 (since m1:m2 = 25:7).
Answer:
The correct option is D, i.e., 25:7.
Introduction:
In a vibration magnetometer, the time-period of magnets when the identical poles are in the same direction is 3 s. When the polarity of the weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets is to be calculated.
Formula Used:
The time-period of oscillation of a magnet in a vibration magnetometer is given by the formula:
T = 2π √(I/mB)
where T is the time-period of oscillation, I is the moment of inertia of the magnet, m is the magnetic moment of the magnet, and B is the magnetic field strength.
Solution:
Let the magnetic moment of the stronger magnet be m1 and that of the weaker magnet be m2.
The given time-period of oscillation when the identical poles are in the same direction is 3 s.
Hence, for the stronger magnet,
T1 = 2π √(I/m1B) = 3
Squaring both sides and simplifying, we get:
m1/T1^2 = I/4π^2B
When the polarity of the weaker magnet is reversed, the combination makes 15 oscillations per minute.
Hence, for the combination of magnets,
T2 = 60/15 = 4 s
The time-period of oscillation for the combination of magnets is given by:
T2 = 2π √(I/(m1 + m2)B)
Squaring both sides and simplifying, we get:
(m1 + m2)/(T2^2 - T1^2) = I/4π^2B
Substituting the values of T1 and T2, and simplifying the above two equations, we get:
m1/T1^2 = (m1 + m2)/(T2^2 - T1^2)
Solving for m2/m1, we get:
m2/m1 = (T2^2 - T1^2)/T1^2
Substituting the given values, we get:
m2/m1 = (16 - 9)/9 = 7/9
Hence, the ratio of magnetic moments of the magnets is 25:7 (since m1:m2 = 25:7).
Answer:
The correct option is D, i.e., 25:7.
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In a vibration magnetometer, the time-period of magnets when the identical poles are in the same directon is 3 s. When the polarity of weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets isa)9:16b)16:9c)7:25d)25:7Correct answer is option 'D'. Can you explain this answer?
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In a vibration magnetometer, the time-period of magnets when the identical poles are in the same directon is 3 s. When the polarity of weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets isa)9:16b)16:9c)7:25d)25:7Correct 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 In a vibration magnetometer, the time-period of magnets when the identical poles are in the same directon is 3 s. When the polarity of weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets isa)9:16b)16:9c)7:25d)25:7Correct 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 In a vibration magnetometer, the time-period of magnets when the identical poles are in the same directon is 3 s. When the polarity of weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets isa)9:16b)16:9c)7:25d)25:7Correct answer is option 'D'. Can you explain this answer?.
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