When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0°, the surface tension of the liquid, in milli Newton m^-1, is__________ $[ρ_{(liquid)} = 900 {kgm}^{- 3}, g = 10 {ms}^{- 2}]$ (Give answer in closest integer)

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answer is 101.

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Detailed Solution

Given : Radius of capillary tube, $r = 0.015 cm = 15 \times 10^{- 5} m$
$h = 15 cm = 15 \times 10^{- 2} m$
Using $h = \frac{2 Tcosθ}{ρgr}$ $[cosθ = \cos 0 ° = 1]$
Surface tension, $T = \frac{rhρg}{2} = \frac{15 \times 10^{- 5} \times 15 \times 10^{- 2} \times 900 \times 10}{2} = 101$ milli newton m^-1