Question

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $3 s$ and $4 s$ 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 }{ MB _{ 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}$
$\frac{ M _1}{ M _2}=\frac{8}{3}$