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)

8 : 3

Answer 2

The correct answer is (B) : 8 : 3
$T=2π\sqrt{\frac{I}{MB_H}}$
$⇒\frac{T_1}{T_2}=\sqrt{\frac{I_1}{I_2}}\sqrt{\frac{M_2}{M_1}}$
$⇒\frac{3}{4}=\sqrt{\frac{3}{2}}\sqrt{\frac{M_2}{M_1}}$
$\frac{M_1}{M_2}=\frac{3}{2}\times\frac{16}{9}$
$=\frac{8}{3}$