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JEE Main 2021 (26 Aug, Shift 1) · Angle of Contact & Capillarity

Angle of Contact & Capillarity question from JEE Main 2021 (26 Aug, Shift 1)

Q49JEE Main 2021 · 26 AUG · SHIFT 1Medium

Angle of Contact & Capillarity

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 ×\times 10−-2 Nm−1{}^{-1}, angle of contact = 0, g = 10 ms2 and density of water = 1.0 ×\times 103 kg m−3{}^{-3}]

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Answer: (b)

  1. Rise in each limb h=2Trρgh = \frac{2T}{r\rho g} with θ=0\theta = 0; r1=2.5 mmr_1 = 2.5\text{ mm}, r2=4.0 mmr_2 = 4.0\text{ mm}.
  2. Δh=2Tρg(1r1−1r2)=2×7.3×10−2103×10(400−250)\Delta h = \frac{2T}{\rho g}\left(\frac{1}{r_1} - \frac{1}{r_2}\right) = \frac{2 \times 7.3\times10^{-2}}{10^3 \times 10}\left(400 - 250\right)
  3. Δh=1.46×10−5×150=2.19×10−3 m\Delta h = 1.46\times10^{-5} \times 150 = 2.19\times10^{-3}\text{ m}
  4. So the answer is (b) 2.19 mm2.19\text{ mm}.
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