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MHT CET 2024 (4 May, Shift 1) · Angle of Contact & Capillarity

Angle of Contact & Capillarity question from MHT CET 2024 (4 May, Shift 1)

Q40MHT CET 2024 · 4 MAY · SHIFT 1Difficult

Angle of Contact & Capillarity

Water rises up to height ' $X$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' d ' in a mine, the water level rises up to height ' $Y$ '. If ' $R$ ' is the radius of earth then the ratio $\frac{Y}{X}$ is

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Answer: (a)

$h = \dfrac{2T\cos\theta}{r\rho g} \Rightarrow h \propto \dfrac{1}{g}$ .
In the mine $g' = g\left(1 - \dfrac{d}{R}\right)$ .
$\dfrac{Y}{X} = \dfrac{g}{g'} = \left(1 - \dfrac{d}{R}\right)^{-1}$ .
So the answer is (a) $\left(1 - \dfrac{d}{R}\right)^{-1}$ .

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