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  4. 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 :

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Q. 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 $10 \Omega$ and air drag negligible, $N$ will be close to :Physics Question Image

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Solution:

$T_{0} = 2 \pi \sqrt{\frac{m}{k}} $
$ = \frac{2\pi}{\sqrt{10}}$
$ A =A_{0}e^{-t/\gamma} $
$ \therefore A =\frac{A_{0}}{e} , t = \gamma$
$ t=\gamma = \frac{2m}{b} = \frac{2m}{\frac{B^{2} \ell^{2}}{R}} = 10^{4} S $
$ \therefore $ No of oscillation $ \frac{t}{T_{0}} = \frac{10^{4}}{2\pi/\sqrt{10}} \approx 5000 $