question_answer

Two bar magnets of the same mass, same length and breadth but having magnetic moments M and 2M are joined together pole for pole and suspended by a string. The time period of assembly in a magnetic field of strength H is 3 seconds. If now the polarity of one of the magnets is reversed and the combination is again made to oscillate in the same field, the time period of oscillation is :

A) \[\sqrt{3}\,\,\,\sec \]

B) \[3\sqrt{3}\,\,\,\sec \]

C)  3 sec

D) 6 sec

Correct Answer: B

Solution :

Time period of magnet oscillating in uniform \[B=T-2\pi \sqrt{\frac{I}{MB}}\]

M = Magnetic moment \[T\propto \frac{1}{\sqrt{M}}\]

\[{{M}_{net}}\] of the combination = \[M+2M=3M\]

\[{{T}_{1}}\propto \frac{1}{\sqrt{3M}}\]

\[{{M}_{net}}\] of the combination \[=2M-M=M\]

\[{{T}_{2}}\propto \frac{1}{\sqrt{M}}\]

\[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{M}{3M}}\]\[\Rightarrow {{T}_{2}}=\sqrt{3}\,\,{{T}_{1}}\]