Physics - Magnetism Question with Solution | TestHub

Let the magnetic moment of magnet $B$ be $M$. Then the magnetic moment of magnet $A$ is $2M$.

Since the magnets are geometrically similar, their moments of inertia are equal. Let $I_A=I_B=I$.

When like poles are kept together, the effective magnetic moment is $M_1=M_A+M_B=2M+M=3M$.

The effective moment of inertia is $I_1=I_A+I_B=2I$.

The time period of oscillation is $T_1=2\pi \sqrt{\frac{I_1}{M_1{B}_H}}=2\pi \sqrt{\frac{2I}{3M{B}_H}}$.

When unlike poles are kept together, the effective magnetic moment is $M_2=M_A-M_B=2M-M=M$.

The effective moment of inertia remains $I_2=I_A+I_B=2I$.

The time period of oscillation is $T_2=2\pi \sqrt{\frac{I_2}{M_2{B}_H}}=2\pi \sqrt{\frac{2I}{M{B}_H}}$.

Taking the ratio of $T_1$ and $T_2$:

$\frac{T_1}{T_2}=\sqrt{\frac{M_2}{M_1}}=\sqrt{\frac{M}{3M}}=\frac{1}{\sqrt{3}}$

Thus, $T_1:T_2=1:\sqrt{3}$.

Answer: $1:\sqrt{3}$