Question

Water rises to a height of 10 cm in capillary tube and mercury falls to a depth of 3.1 cm in the same capillary tube. If the density of mercury is 13.6 and the angle of contact for mercury is 135°, the approximate ratio of surface tensions of water and mercury is(a) 1 : 0.15(b) 1 : 3(c) 1 : 6(d) 1.5 : 1

Answer 1

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Answer 2

Answer:

C) 1:6

Explanation:

Height = 10cm (Given)

Fall rate of mercury = 3.1cm ( Given)

Let a liquid of density ρ rise a height h in a capillary of radius r

Thus,

h = 2Tcosθ/rpg

Where T is surface tension of that liquid,θ is angle of contact and θw will be the angle of contact of water. Let Tm and Tw be the surface tension of water and mercury.

Tw/Tm = (rhρg/2cosθ)/(r'h'ρ'g'/2cosθ')

           = hρcosθ/ h'ρ'cosθ

           = 10×1×cos135°/ -3.42×13.6× cos0°

           = 5r2/3.42×13.6

           = 1/6.5

Thus, the approximate ratio of surface tensions of water and mercury is 1:6