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MHT CET 2025 (26 Apr, Shift 1) · Angle of Contact & Capillarity

Angle of Contact & Capillarity question from MHT CET 2025 (26 Apr, Shift 1)

Q28MHT CET 2025 · 26 APR · SHIFT 1Medium

Angle of Contact & Capillarity

A capillary tube when immersed vertically in water, the rise of water column is upto height h1h_1 on earth's surface. When this arrangement is taken into a mine of depth 'd', below earth's surface, the height of the water column is h2h_2. If R is the radius of the earth, the ratio h2h1\frac{h_2}{h_1} is

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Answer: (d)

  1. h=2Tcos⁡θrρg⇒h∝1gh = \dfrac{2T\cos\theta}{r\rho g} \Rightarrow h \propto \dfrac{1}{g}.
  2. In a mine of depth dd: g′=g(1−dR)=g R−dRg' = g\left(1 - \dfrac{d}{R}\right) = g\,\dfrac{R-d}{R}.
  3. h2h1=gg′=RR−d\dfrac{h_2}{h_1} = \dfrac{g}{g'} = \dfrac{R}{R-d}.
  4. So the answer is (d) RR−d\dfrac{R}{R-d}.
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