Question

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

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

The correct option is C $\frac{1}{\sqrt{3}}$

As we know that,

$T_{Sum}=2\pi \sqrt{\frac{(I_1+I_2)}{(M_1+M_2)B_H}}$,

$T_{diff}=2\pi \sqrt{\frac{I_1+I_2}{(M_1-M_2)B_H}}$

$\Rightarrow \frac{T_s}{T_d}=\frac{T_1}{T_2}=\sqrt{\frac{M_1-M_2}{M_1+M_2}}=\sqrt{\frac{2M-M}{2M+M}}=\frac{1}{\sqrt{3}}$