Question

A magnetic dipole of magnetic moment $6 \times 10^{-2} \, Am^{2}$ and moment of inertia $12 \times 10^{-6} \, kg\, m^{2}$ performs oscillations in a magnetic field of $2 \times 10^{-2} $ T. The time taken by the dipole to complete $20$ oscillations is $( \pi \simeq 3)$

• A. 36 s
• B. 6 s
• C. 12 s
• D. 18 s

Answer 1

Answer: (C)

Given,
Magnetic moment $(M)=6 \times 10^{-2} \,A - m ^{2}$
Moment of inertia $(I)=12 \times 10^{-6} kg - m ^{2}$
Magnetic field $(B)=2 \times 10^{-2} T$
We know that. Time $(t)=2 \pi \sqrt{\frac{I}{M B}}$
$=2 \pi \sqrt{\frac{12 \times 10^{-6}}{6 . \times 10^{-2} \times 2 \times 10^{-2}}} $
$=2 \pi \sqrt{\frac{12 \times 10^{-2}}{12}} $
$=2 \pi \times 10^{-1}$
For 20 oscillation,
Time $(t)=20 \times 2 \pi \times 10^{-1}$
$=12 s$