Physics - Magnetism Question with Solution | TestHub

Frequency at the first place, $f_1=\frac{30}{60}=\frac{1}{2}\text{ Hz}$

Time period at the first place, $T_1=\frac{1}{f_1}=2\text{ s}$

Let the magnetic induction at the first place be $B_1$.

Since the magnetic induction at the second place is increased by two times the magnetic induction at the first place, $B_2=B_1+2B_1=3B_1$.

The time period of a magnet is given by $T=2\pi \sqrt{\frac{I}{MB}}$, which implies $T\propto \frac{1}{\sqrt{B}}$.

$\frac{T_2}{T_1}=\sqrt{\frac{B_1}{B_2}}$

$T_2=2\sqrt{\frac{B_1}{3B_1}}=\frac{2}{\sqrt{3}}\text{ s}$

Answer: $\frac{2}{\sqrt{3}}\mathrm{s}$