Question

At a certain place, a magnet makes $30$ oscillations per min. At another place, where the magnetic field is double, its time period will be:

• A. $4s$
• B. $2s$
• C. $\frac{1}{2}s$
• D. $\sqrt{2}s$

Answer 1

The correct option is D $\sqrt{2}s$

Let the magnetic field at first place be $B$ :

Time period of oscillation at first place : $T_1=\frac{60}{30}=2$ $s$

Using $T=2\pi \sqrt{\frac{1}{mB}}$

$⟹$ $\frac{T_1^2}{T_2^2}=\frac{B_2}{B_1}$

$\therefore$ $\frac{2^2}{T_2^2}=\frac{2B}{B}$

OR $T_2^2=2$ $⟹T_2=\sqrt{2}$ $s$