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Question:

A thin strip 10 cm long is on a U-shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm⁻¹. The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10Ω and air drag is negligible, N will be close to

5000

50000

10000

1000

Solution:

Correct option is B. 5000
T₀ = 2π√(m/k) = 2π√(10⁻² / 0.5) = 2π/10
A = A₀e⁻ᵗ/γ
∴ for A = A₀/e, t = γ
γ = 2m/b = 2m(B²l²/R) = 10⁴s
∴ No of oscillations = t/T₀ = 10⁴ / (2π/10) ≈ 5000.