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  4. A bar magnet suspended freely in a uniform magnetic field is vibrating with a time period of 3 s . If the field strength is increased to 4 times of the earlier field strength, the time period will be (in seconds)

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Q. A bar magnet suspended freely in a uniform magnetic field is vibrating with a time period of $ 3\,s $ . If the field strength is increased to $ 4 $ times of the earlier field strength, the time period will be (in seconds)

Punjab PMETPunjab PMET 2008Magnetism and Matter

Solution:

$T=2 \pi \sqrt{\frac{1}{M B}}$
or $T \propto \frac{1}{\sqrt{B}}$ or $\frac{T_{2}}{T_{1}}=\sqrt{\frac{B_{1}}{B_{2}}}$
or $\frac{T_{2}}{T_{3}}=\sqrt{\frac{1}{4}}$ or $T_{2}=1.5\, s$