Water rises to a height of 10cm in a capillary tube and mercury falls to a depth of 3.42 cm in the same capillary tube. If the density of mercury is 13.6g/cc and the angle of contact of mercury and water are 135° and 0° respectively, the ratio of surface tension of water and mercury is

Q: Water rises to a height of 10cm in a capillary tube and mercury falls to a depth of 3.42 cm in the same capillary tube. If the density of mercury is 13.6g/cc and the angle of contact of mercury and water are 135° and 0° respectively, the ratio of surface tension of water and mercury is
(A) 1 : 0.15
(B) 1 : 3
(C) 1 : 6.5
(D) 1.5 : 1

Solution: h =2Scosθ/ρgr
or S =hρgr/2cosθ
or S ∝ hρ/cosθ
Sw/SHg = h1/h2 × ρ12 × cosθ1/cosθ2
Putting the values, we obtain 1 : 6.5
Hence, (C) is correct.

Author: Rajesh Jha

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