A) \[{{T}_{1}}<{{T}_{2}}\]
B) \[{{T}_{1}}>{{T}_{2}}\]
C) \[{{T}_{1}}={{T}_{2}}\]
D) \[{{T}_{2}}=\infty ,\,{{T}_{1}}=0\]
Correct Answer: A
Solution :
Using the formula for time period for magnetic system \[T=2\pi \sqrt{\left( \frac{I}{mH} \right)}\] \[\Rightarrow \] \[T\propto \frac{1}{\sqrt{M}}\] ??(i) When similar poles placed at same side, then \[{{M}_{1}}=M+2M-M=3M\] So, from Eq. (i) \[{{T}_{2}}\propto \frac{1}{\sqrt{3M}}\] ?...(ii) When the polarity of a magnet is reversed, then \[{{M}_{2}}=2M-M=M\] So, from Eq. (i) \[{{T}_{2}}\propto \frac{1}{\sqrt{M}}\] ??(iii) Now, dividing Eq. (ii) by Eq. (iii), we get \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{\sqrt{M}}{\sqrt{3M}}\] \[=\frac{1}{\sqrt{3}}\] \[\Rightarrow \] \[{{T}_{2}}=\sqrt{3}{{T}_{1}}\] Hence, \[{{T}_{1}}<{{T}_{2}}\]
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