At a certain place a magnet makes 30 oscillations per minute. At another place where the magnetic field is…

At a certain place a magnet makes 30 oscillations per minute. At another place where the magnetic field is double, its time period will be
  1. $4 \mathrm{~s}$
  2. $2 \mathrm{~s}$
  3. $\frac{1}{2} \mathrm{~s}$
  4. $\sqrt{2} \mathrm{~s}$

Solution

$\begin{aligned} T=2 \pi & \sqrt{\frac{I}{M B_H}} \\ \therefore \quad \frac{T_1}{T_2} & =\sqrt{\frac{\left(B_H\right)_2}{\left(B_H\right)_1}} \\ T_2 & =T_1 \sqrt{\frac{\left(B_H\right)_1}{\left(B_H\right)_2}} \\ n_1 & =30 \text { oscillation } / \mathrm{min} \\ n_1 & =\frac{1}{2} \text { oscillation } / \mathrm{s} \\ T_1 & =2 \mathrm{~s} \\ T_2 & =2 \sqrt{\frac{B_H}{2 B_H}} \\ = & 2 \times \frac{1}{\sqrt{2}}=\sqrt{2} \mathrm{~s}\end{aligned}$

Asked in: AP EAMCET 2012

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