First slide

Surface tension

Question

Two capillary tubes made of same material having radii r and 2r are vertically dipped in the same liquid. Then due to capillary rise

Moderate

A

masses of water due to capillary rise in the tubes will be the same
B

capillary rise in the tubes are same
C

masses of water in the tubes are in the ratio 1:2
D

capillary rise in the tubes are in the ratio 1:2

Solution

Capillary rise $h = \frac{2 Tcosθ}{ρrg} \Rightarrow h \propto \frac{l}{r}$
Mass of water in the tube, $m = {πr}^{2} . h . ρ = {πr}^{2} [\frac{2 Tcosθ}{ρrg}] . ρ = \frac{2 πTrcosθ}{g}$
For same material of tube and same liquid, angle of contact is the same. Therefore $m \propto r$
Ratio of capillary rise, $h_{1} : h_{2} = 2 : 1$

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