Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2, then the ratio of their magnetic moments will be :
Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2, then the ratio of their magnetic moments will be :
2 : 1
8 : 3
1 : 3
27 : 16
The Correct Option is B
Solution and Explanation
The correct answer is (B) : 8 : 3
\(T=2π\sqrt{\frac{I}{MB_H}}\)
\(⇒\frac{T_1}{T_2}=\sqrt{\frac{I_1}{I_2}}\sqrt{\frac{M_2}{M_1}}\)
\(⇒\frac{3}{4}=\sqrt{\frac{3}{2}}\sqrt{\frac{M_2}{M_1}}\)
\(\frac{M_1}{M_2}=\frac{3}{2}\times\frac{16}{9}\)
\(=\frac{8}{3}\)
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
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Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.