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Physics Question on Magnetism and matter

A magnetic dipole of magnetic moment 6×10−2 Am26 \times 10^{-2} \, {Am^{2}} and moment of inertia 12×10−6 kg m212 \times 10^{-6} \, {kg\, m^{2}} performs oscillations in a magnetic field of 2×10−22 \times 10^{-2} T. The time taken by the dipole to complete 2020 oscillations is (π≃3)( \pi \simeq 3)

A

36 s

B

6 s

C

12 s

D

18 s

Answer

12 s

Explanation

Solution

Given, Magnetic moment (M)=6×10−2 A−m2(M)=6 \times 10^{-2} \,A - m ^{2} Moment of inertia (I)=12×10−6kg−m2(I)=12 \times 10^{-6} kg - m ^{2} Magnetic field (B)=2×10−2T(B)=2 \times 10^{-2} T We know that. Time (t)=2πIMB(t)=2 \pi \sqrt{\frac{I}{M B}} =2π12×10−66.×10−2×2×10−2=2 \pi \sqrt{\frac{12 \times 10^{-6}}{6 . \times 10^{-2} \times 2 \times 10^{-2}}} =2π12×10−212=2 \pi \sqrt{\frac{12 \times 10^{-2}}{12}} =2π×10−1=2 \pi \times 10^{-1} For 20 oscillation, Time (t)=20×2π×10−1(t)=20 \times 2 \pi \times 10^{-1} =12s=12 s