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

At certain place a magnet makes 30 oscillations per minute. At another place if the magnetic induction is increased by two times the magnetic induction at first place, then the time period of same magnet will be
  1. $\frac{2}{\sqrt{3}} \mathrm{~s}$
  2. $2 \sqrt{3} \mathrm{~s}$
  3. $\frac{\sqrt{3}}{2} \mathrm{~s}$
  4. $\quad \sqrt{3} \mathrm{~s}$

Solution

$T=2 \pi \sqrt{\frac{I}{M B}} \Rightarrow T \propto \frac{1}{\sqrt{B}}$
Given $\mathrm{n}_1=30$ osc. $/ \mathrm{min} \Rightarrow \mathrm{T}_1=2 \mathrm{~s}$ $\therefore \quad \frac{\mathrm{T}_2}{\mathrm{~T}_1}=\frac{\sqrt{\mathrm{B}_1}}{\sqrt{\mathrm{~B}_2}}$ Now, $\mathrm{B}_2=\mathrm{B}_1+2 \mathrm{~B}_1=3 \mathrm{~B}_1$ $\therefore \quad \frac{\mathrm{T}_2}{\mathrm{~T}_1}=\sqrt{\frac{\mathrm{B}_1}{3 \mathrm{~B}_1}}=\frac{1}{\sqrt{3}} \Rightarrow \mathrm{~T}_2=\frac{1}{\sqrt{3}} \times 2=\frac{2}{\sqrt{3}} \mathrm{~s}$

Asked in: MHT CET 2024 (02 May Shift 1)

Practice more Magnetic Effects of Current questions on Aicharya