A) \[{{T}_{1}}<{{T}_{2}}\]
B) \[{{T}_{1}}>{{T}_{2}}\]
C) \[{{T}_{1}}={{T}_{2}}\]
D) \[{{T}_{2}}=\] \[\infty \]
Correct Answer: A
Solution :
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 \[{{M}_{2}}=2M-M=M\] \[\therefore {{T}_{2}}=2\pi \sqrt{\frac{I}{{{M}_{2}}H}}=2\pi \sqrt{\frac{I}{M\,H}}....(ii)\] From Eqs. (i) and (ii), we observe that \[{{T}_{1}}<{{T}_{2}}\]
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