Question

A magnet is suspended in the magnetic meridian with an untwisted wire. The upper end of the wire is rotated through 180${}^0$ to deflect the magnet through 30${}^0$ from the magnetic meridian. When the magnet is replaced by another magnet, the upper end of the wire is rotated through 270${}^0$ to deflect the magnet 30${}^0$ from the magnetic meridian. The ratio of the magnetic moments is (nearly)

• A. 1:1
• B. 8:5
• C. 2:3
• D. 5:8

Answer 1

The correct option is D 5:8

the torque applied by the string is directly proportional to total angle of deflection.
in case 1,
${180}^0-{30}^0={150}^0$
in case 2,
${270}^0-{30}^0={240}^0$
hence,
$k\ast {150}^0=M_{1}Bsin{30}^0$
$k\ast {240}^0=M_{2}Bsin{30}^0$
$\therefore \frac{M_1}{M_2}=\frac{150}{240}=\frac{5}{8}$