A) \[{{T}_{1}}<{{T}_{2}}\]
B) \[{{T}_{1}}>{{T}_{2}}\]
C) \[{{T}_{1}}={{T}_{2}}\]
D) \[{{T}_{2}}=\,\infty \]
Correct Answer: A
Solution :
[a] The time period of bar magnet |
\[T=2\pi \sqrt{\frac{I}{MH}}\] |
where M= magnetic moment of magnet |
I = moment of inertia and |
H = horizontal component of magnetic field |
When same poles of magnets are placed on same side, then net magnetic moment |
\[{{M}_{1}}=M+2M=3M\] |
\[\therefore \] \[T{{ & }_{1}}=2\pi \,\sqrt{\frac{I}{{{M}_{1}}H}}\] |
\[=2\pi \,\sqrt{\frac{I}{3\,M\,H}}\] ....(i) |
When opposite poles of magnets are placed on same side, then net magnetic moment |
\[{{M}_{2}}=2MM~=M\] |
\[\therefore \] \[{{T}_{2}}=2\pi \sqrt{\frac{I}{{{M}_{2}}H}}=2\pi \sqrt{\frac{I}{M\,H}}\] (ii) |
From Eqs. (i) and (ii), we observe that |
\[{{T}_{1}}<{{T}_{2}}\] |
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