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Magnets A and B are geometrically similar but a magnetic moment of A is twice that of B. If T₁ and T₂ is the time periods of the oscillation when their like poles and unlike poles kept together respectively, then $\frac{T_1}{T_2}$ will be:
Option: 1
$\frac{1}{3}$

Option: 2
$\frac{1}{2}$

Option: 3
$\frac{1}{\sqrt{3}}$

Option: 4
$\sqrt{3}$

Answers (1)

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As we learn

Ratio of difference and sum position of magnetic moment -

$\frac{T_{s}}{t_{d}}=\sqrt{\frac{M_{1}-M_{2}}{M_{1}+M_{2}}}$

$\frac{M_{1}}{M_{2}}=\frac{T_{d}^{2}+T_{s}^{2}}{T_{d}^{2}-T_{s}^{2}}$

$\frac{\nu _{s}^{2}+ \nu _{d}^{2}}{\nu _{s}^{2}-\nu _{d}^{2}}$

-

Tsum = $2\pi$ $\sqrt{\frac{(I_{1} + I_{2})}{(M_{1}+M_{2})B_H}}$

T_diff = $2\pi$ $\sqrt{\frac{I_{1} + I_{2}}{(M_{1}-M_{2})B_H}}$

$\Rightarrow$ $\frac{T_s}{T_d}$ $=\frac{T_{1}}{T_{2}}$ $=\sqrt{\frac{M_{1}-M_{2}}{M_{1}+ M_{2}}}$ $=\sqrt{\frac{2M-M}{2M+M}}$ $=\frac{1}{\sqrt{3}}$

Posted by

Gautam harsolia

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