A glass rod of radius ' r₁ ' is inserted symmetrically into a… | MHT CET 2021 (23 Sep, Shift 2)

Q52MHT CET 2021 · 23 SEP · SHIFT 2Difficult

Angle of Contact & Capillarity

A glass rod of radius ' $r_1$ ' is inserted symmetrically into a vertical capillary tube of radius ' $r_2$ ' ( $r_1 < r_2$ ) such that their lower ends are at same level. The arrangement is dipped in water. The height to which water will rise into the tube will be ( $\rho =$ density of water, T = surface tension in water, g = acceleration due to gravity)

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Answer: (a)

Surface tension acts along both the tube wall (perimeter $2\pi r_2$ ) and the rod (perimeter $2\pi r_1$ ): $F = 2\pi T(r_1 + r_2)$ .
Weight of water in the gap: $W = \pi(r_2^2 - r_1^2)h\rho g$ .
$F = W \Rightarrow h = \dfrac{2T(r_1 + r_2)}{(r_2 - r_1)(r_2 + r_1)\rho g} = \dfrac{2T}{(r_2 - r_1)\rho g}$ .
So the answer is (a) $\dfrac{2T}{(r_2 - r_1)\rho g}$ .

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