Question

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $3s$ and $4s$ respectively. If their moments of inertia are in the ratio of $3:2$ then the ratio of their magnetic moments will be :

• A. $2:1$
• B. $8:3$
• C. $1:3$
• D. $27:16$

Answer 1

Answer: (B)

$T=2\pi \sqrt{\frac{I}{M{B}_H}}$
$\frac{T_1}{T_2}=\frac{2\pi \sqrt{\frac{I_1}{M_1{B}_H}}}{2\pi \sqrt{\frac{I_2}{M_2{B}_H}}}=\frac{3}{4}$
$\sqrt{\frac{I_1}{I_2}\times \frac{M_2}{M_1}}=\frac{3}{4}$
$\sqrt{\frac{I_1}{I_2}}\times \sqrt{\frac{M_2}{M_1}}=\frac{3}{4}$
$\sqrt{\frac{3}{2}}\times \sqrt{\frac{M_2}{M_1}}=\frac{3}{4}$
$\frac{3}{2}\times \frac{M_2}{M_1}=\frac{9}{16}$
$\frac{M_1}{M_2}=\frac{8}{3}$