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JEE Main 2020 (7 Jan, Shift 1) · Speed of Waves

Speed of Waves question from JEE Main 2020 (7 Jan, Shift 1)

Q31JEE Main 2020 · 7 JAN · SHIFT 1Difficult

Speed of Waves

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 ×\times 1011 Nm-2, the extension of wire over its natural length is:

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Answer: (a)

  1. μ=6×10−3/0.6=0.01\mu = 6\times10^{-3}/0.6 = 0.01 kg/m, so T=μv2=0.01×902=81T = \mu v^2 = 0.01 \times 90^2 = 81 N.
  2. Δl=TLAY=81×0.610−6×16×1011=3.0×10−5\Delta l = \dfrac{TL}{AY} = \dfrac{81 \times 0.6}{10^{-6} \times 16\times10^{11}} = 3.0\times10^{-5} m
  3. So the answer is (a) 0.03 mm.
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