Question

A bar magnet of moment of inertia $9 \times 10^{-5} \; kg\,m^2$ placed in a vibration magnetometer and oscillating in a uniform magnetic field $16 \pi^2 \times 10^{-5} T$ makes $20$ oscillations in $15 \,s$. The magnetic moment of the bar magnet is

• A. $3 \, A-m^2$
• B. $2 \, A-m^2$
• C. $ 5 \, A-m^2$
• D. $6 \,A-m^2$
• E. $ 4 \, A-m^2$

Answer 1

Answer: (E)

Given,
$I=9 \times 10^{-5}\, kg - m ^{2} $
$B=16 \,\pi^{2} \times 10^{-5} \,T $
$T=\frac{15}{20}=0.75$
The time period
$T =2 \pi \sqrt{\frac{I}{M B}} $
$ T^{2} =4 \pi^{2} \times \frac{I}{M B} $
$M =4 \pi^{2} \times \frac{I}{T^{2} B} $
$=4 \pi^{2} \times \frac{9 \times 10^{-5}}{16 \pi^{2} \times 10^{-5} \times(0.75)^{2}}$
$=\frac{9}{4 \times 0.5625}$
$=\frac{9.00}{2.25}=4 \,A - m ^{2}$