A magnetic dipole of magnetic moment 6 × 10-2 Am2 and moment of inertia 12 × 10-6 kg m2 performs oscillations in a magnetic field of 2 × 10-2 T. The time taken by the dipole to complete 20 oscillations is ( π ≃ 3)

Question

A magnetic dipole of magnetic moment 6 × 10-2 Am2 and moment of inertia 12 × 10-6 kg m2 performs oscillations in a magnetic field of 2 × 10-2 T. The time taken by the dipole to complete 20 oscillations is ( π ≃ 3) (A) 36 s (B) 6 s (C) 12 s (D) 18 s

Tardigrade Admin · Accepted Answer

Given, Magnetic moment (M)=6 × 10-2 A - m 2 Moment of inertia (I)=12 × 10-6 kg - m 2 Magnetic field (B)=2 × 10-2 T We know that. Time (t)=2 π √(I/M B) =2 π √(12 × 10-6/6 . × 10-2 × 2 × 10-2) =2 π √(12 × 10-2/12) =2 π × 10-1 For 20 oscillation, Time (t)=20 × 2 π × 10-1 =12 s

Q. A magnetic dipole of magnetic moment 6×10−2Am2 and moment of inertia 12×10−6kgm2 performs oscillations in a magnetic field of 2×10−2 T. The time taken by the dipole to complete 20 oscillations is (π≃3)

36 s

6 s

12 s

18 s

Given, Magnetic moment (M)=6×10−2A−m2 Moment of inertia (I)=12×10−6kg−m2 Magnetic field (B)=2×10−2T We know that. Time (t)=2πMBI​​ =2π6.×10−2×2×10−212×10−6​​ =2π1212×10−2​​ =2π×10−1 For 20 oscillation, Time (t)=20×2π×10−1 =12s

Q. A magnetic dipole of magnetic moment $6 \times 1 0^{- 2} A m^{2}$ and moment of inertia $12 \times 1 0^{- 6} k g m^{2}$ performs oscillations in a magnetic field of $2 \times 1 0^{- 2}$ T. The time taken by the dipole to complete $20$ oscillations is $(π ≃ 3)$