• 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

 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}}$