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 (see figure). 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 oscillation it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 Ω and air drag negligible, N will be close to :

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 (see figure). 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 oscillation it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 Ω and air drag negligible, N will be close to : (A) 50000 (B) 5000 (C) 10000 (D) 1000

Tardigrade Admin · Accepted Answer

T0 = 2 π √(m/k) = (2π/√10) A =A0e-t/&gamma; ∴ A =(A0/e) , t = &gamma; t=&gamma; = (2m/b) = (2m/(B2 ℓ2)R) = 104 S ∴ No of oscillation (t/T0) = (104/2π/√10) ≈ 5000

50000

5000

10000

1000

T0​=2πkm​​ =10​2π​ A=A0​e−t/γ ∴A=eA0​​,t=γ t=γ=b2m​=RB2ℓ2​2m​=104S ∴ No of oscillation T0​t​=2π/10​104​≈5000

$T_{0} = 2 π \frac{m}{k}$
$= \frac{2 π}{10}$
$A = A_{0} e^{- t / γ}$
$∴ A = \frac{A _{0}}{e}, t = γ$
$t = γ = \frac{2 m}{b} = \frac{2 m}{\frac{B ^{2} ℓ ^{2}}{R}} = 1 0^{4} S$
$∴$ No of oscillation $\frac{t}{T _{0}} = \frac{1 0 ^{4}}{2 π / 10} \approx 5000$