KVPY Sample Paper KVPY Stream-SX Model Paper-30

A magnet is suspended in the magnetic meridian with an untwisted wire. The upper end of the wire is rotated through \[180{}^\circ \] to deflect the magnet by \[30{}^\circ \] from magnetic meridian. Now this magnet is replaced by another magnet and the upper end of the wire has to be rotated through \[270{}^\circ \] to deflect the magnet by \[30{}^\circ \] from magnetic meridian. The ratio of magnetic moments of the two magnet is -

A) 1 : 1

B) \[\frac{2}{3}\]

C) \[\frac{3}{2}\]

D) \[\frac{5}{8}\]

Correct Answer: D

Solution :

for Ist magnet twist in spring \[=180-30\] and this twist produce restoring torque magnet will finally stay in equailibrium position where both magnetic torque of horizontal component of earth magnetic field and spring torque are balanced
\[C\,\,[180-30]={{M}_{1}}{{B}_{H}}\sin 30{}^\circ \]	...(1)
for IInd magnet
\[C\,\,[270-30]={{M}_{2}}{{B}_{H}}\sin 30{}^\circ \]	...(2)
from (1) and (2)
\[\frac{{{M}_{1}}}{{{M}_{2}}}=\frac{150}{240}=\frac{5}{8}\]
\[\frac{{{M}_{1}}}{{{M}_{2}}}=\frac{5}{8}\]