A short bar magnet having magnetic moment 4 Am², placed in a vibrating magneto meter, vibrates with a time period of 8 seconds. Another short bar magnet having a magnetic moment 8 Am² vibrates with a time period of 6 seconds. If the moment of inertia of the second magnet is 9 x 10^-2kg m² the moment of inertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field)
Correct answer: B. 8 x 10^-2 kg m2
- A. 9 x 10^-2 kg m2
- B. 8 x 10^-2 kg m2
- C. 5.33 x 10^-2 kg m2
- D. 12.2 x 10^-2 kg m2
Explanation
Relate the moment of inertia (I) to the time period (T) and magnetic moment (μ) for a magnet in a vibrating magnetometer:The equation is:T² = (I * π²) / (μ * B)where:T is the time period (seconds)I is the moment of inertia (kg m²)μ is the magnetic moment (Am²)B is the magnetic field strength (T)Analyze the given information:The magnetic moment of the first magnet (μ₁) is 4 Am².The time period of the first magnet (T₁) is 8 seconds.The magnetic moment of the second magnet (μ₂) is 8 Am².The time period of the second magnet (T₂) is 6 seconds.The moment of inertia of the second magnet (I₂) is 9 x 10^-2 kg m².We are asked to find the moment of inertia of the first magnet (I₁).Solve for I₁:We can rewrite the equation to isolate I₁:I₁ = (T₁² * μ₁ * B) / π²Since both magnets are in the same uniform magnetic field (B), we can eliminate B from the equation. Additionally, the ratio of B cancels out when we divide the equation for I₂ by the equation for I₁:I₁ / I₂ = (T₁² * μ₁) / (T₂² * μ₂)Plug in the known values and solve:I₁ / (9 x 10^-2 kg m²) = (8 s)² * (4 Am²) / (6 s)² * (8 Am²)I₁ ≈ 8 x 10^-2 kg m²Therefore, the moment of inertia of the first magnet is 8 x 10^-2 kg m². This matches with answer choice b
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Electromagnetism
Magnetic flux density and magnetic flux describe the strength of a magnetic field and the field passing through a surface. A charged particle moving through a magnetic field experiences a force perpendicular to its velocity and may follow circular or helical motion, depending on the angle between velocity and field.
Practise Electromagnetism
1,176 free Electromagnetism MCQs from Physics, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Physics questions like this
Physics is on 16 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Electromagnetism questions
Cause of heat production in a current carrying conductors is:
The force on electron in electric field of 108 N/C is:
In a step-up transformer when the alternating voltage increases then the alternating current:
Two short bar magnets have their magnetic moments 1.2Am² and1.0 Am². They are placed on a horizontal table parallel to each other at a distance of 20 cm between their centers, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth's field is 3.6 * 10 ^ - 5 * T T.then,the resultant horizontal magnetic induction at mid-point of the line joining their centers
an electron of charge e coulomb passes through a potential difference of V volts. its energy in joules will be
the resistance of voltmeter must have very high resistance because