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MHT CET 2023 (9 May, Shift 1) · Motional EMF

Motional EMF question from MHT CET 2023 (9 May, Shift 1)

Q29MHT CET 2023 · 9 MAY · SHIFT 1Medium

Motional EMF

A conducting wire of length 2500 m2500\text{ m} is kept in east-west direction, at a height of 10 m10\text{ m} from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire =252 Ω= 25\sqrt{2}\ \Omega, acceleration due to gravity g=10 m/s2, BH=2×10−5 Tg = 10\text{ m/s}^{2},\ B_H = 2 \times 10^{-5}\text{ T})

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Answer: (b)

  1. Speed on reaching the ground: v=2gh=2×10×10=102v = \sqrt{2gh} = \sqrt{2\times10\times10} = 10\sqrt2 m/s.
  2. ε=BHlv=2×10−5×2500×102=0.52\varepsilon = B_H l v = 2\times10^{-5} \times 2500 \times 10\sqrt2 = 0.5\sqrt2 V.
  3. I=εR=0.52252=0.02I = \frac{\varepsilon}{R} = \frac{0.5\sqrt2}{25\sqrt2} = 0.02 A
  4. So the answer is (b) 0.020.02 A.
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