A magnetic needle of magnetic moment 6.7 × 10-2 Am2 and moment of inertia 7.5 × 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is :

Question

A magnetic needle of magnetic moment 6.7 × 10-2 Am2 and moment of inertia 7.5 × 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is : (A) 6.65 s (B) 8.89 s (C) 6.98 s (D) 8.76 s

Tardigrade Admin · Accepted Answer

T = 2 π √(I/MB) = 2π √(7.5 ×10-6/6.7 ×10-2 ×0.01) = (2π/10) ×1.06 For 10 oscillations, t = 10 T = 2π ×1.06 = 6.6568 ≈6.65 s

Q. A magnetic needle of magnetic moment $6.7 \times 1 0^{- 2} A m^{2}$ and moment of inertia $7.5 \times 1 0^{- 6} k g m^{2}$ is performing simple harmonic oscillations in a magnetic field of $0.01 T$ . Time taken for $10$ complete oscillations is :

6.65 s

8.89 s

6.98 s

8.76 s

$T = 2 π \frac{I}{MB}$
$= 2 π \frac{7.5 \times 1 0 ^{- 6}}{6.7 \times 1 0 ^{- 2} \times 0.01} = \frac{2 π}{10} \times 1.06$
For 10 oscillations,
$t = 10 T = 2 π \times 1.06$
$= 6.6568 \approx 6.65 s$

Q. A magnetic needle of magnetic moment 6.7×10−2Am2 and moment of inertia 7.5×10−6kgm2 is performing simple harmonic oscillations in a magnetic field of 0.01T. Time taken for 10 complete oscillations is :