Question:

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

8.76s

8.89s

6.65s

6.98s

T=mBsinθ=Id²θ/dt²
mBθ=Id²θ/dt² → ω=√(mB/I)
T=2πω=2π√(I/mB)
=10 × 2π√(7.5 × 10⁻⁶ / 6.7 × 10⁻⁶ × 0.01)
=10 × 2 × 3.14 × √(7.5 / 6.7 × 0.01)
=6.65s