Question

The magnetic moments of two bar magnets of same size are in the ratio $1:2$. When they are placed one over the other with their poles together, then their period of oscillation in a magnetic field is $3s$. if one the magnets is reversed, then the period of oscillation in the same field will be:

• A. $\sqrt{3}s$
• B. $3\sqrt{3}s$
• C. $3s$
• D. $6s$

Answer 1

The correct option is B $3\sqrt{3}s$

Time period of oscillation is given by $T=2\pi \sqrt{\frac{I}{MB}}$

Where I is the moment of inertia and B is the magnetic field.

When they are placed one over the other with their poles together, then magnetic moment is $M_1=x+2x=3x$ where x is the magnetic moment. The period of oscillation in a magnetic field is 3s.

So time period is $3=2\pi \sqrt{\frac{I}{3xB}}...........\left(1\right)$

When polarity is reversed than the net magnetic field is $M_2=x$

So, time period is $T_2=2\pi \sqrt{\frac{I}{xB}}...........\left(2\right)$

Taking ratios of (1) and (2)

$\frac{9}{{T_2}^2}=\frac{4{\pi }^2\frac{I}{3xB}}{4{\pi }^2\frac{I}{xB}}$

$\frac{9}{{T_2}^2}=\frac{1}{3}$

${T_2}^2=27$

$T_2=3\sqrt{3}s$