A thin strip 10cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5N m ^ - 1 (see figure). The assembly is kept in a uniform magnetic field of 0.1T . If the strip

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Quantrex Academy · Accepted Answer

Correct answer: B. 5000

Equation of motion for slider: - m d ^ 2 x d t ^ 2 = kx + ilB m d ^ 2 x d t ^ 2 + kx + ((Blv)/(R))lB = 0 ⇒ m d ^ 2 x d t ^ 2 + B ^ 2 l ^ 2 R . (dx)/(dt) + kx = 0 Comparing with m d ^ 2 x d t ^ 2 + b . (dx)/(dt) + kx = 0 m = m; b = B ^ 2 l ^ 2 R ; k = k We know: A = A _ 0 e ^ (- b)/(2m) × t = A _ 0 e ^ - B ^ 2 l ^ 2 2mR × t For amplitude to be A _ 0 / e, A _ 0 e ^ - B ^ 2 l ^ 2 2mR × t = (A)/(e) ⇒ B ^ 2 l ^ 2 2mR × t = 1 t = 2mR B ^ 2 l ^ 2 = 10,000sec Time period = 2π (m)/(k) = 2s Number of oscillations = (10,000)/(2) = 5,000

A thin strip 10cm long is on a U shaped wire of negligible...

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