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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Magnetic Properties of Matter

JEE Main · Physics · Magnetic Properties of Matter

At a certain place a magnet makes 30 oscillations per minute. At...

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

Options

  1. A4 s4 \mathrm{~s}
  2. B2 s2 \mathrm{~s}
  3. C12 s\frac{1}{2} \mathrm{~s}
  4. D2 s\sqrt{2} \mathrm{~s}

Correct answer

D. 2 s\sqrt{2} \mathrm{~s}

Step-by-step solution

T=2πIMBH∴T1T2=(BH)2(BH)1T2=T1(BH)1(BH)2n1=30 oscillation /min⁡n1=12 oscillation /sT1=2 sT2=2BH2BH=2×12=2 s\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}
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