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Question

Water rises to a height of 10 cm in a certain capillary tube. Another identical tube when dipped in mercury, the level of mercury is depressed by 3.42 cm. Density of mercury is 13.6 gm/cm3. The angle of contact for water in contact with glass is 0 and mercury in contact with glass is 135. Then the ratio of surface tension of water to that of mercury is:
(use 0.03422=0.024)

A
0.33
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B
0.25
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C
0.75
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D
0.15
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Solution

The correct option is D 0.15
For Water:
Rise in height, h1=10cm=0.1 m
Density of water, ρ1=1000kg/m3
Angle of contact, θ1=0
radius of tube=r
Surface Tension=T1
h=2Tcosθρgr ...(i)

h1=2T1cosθ1ρ1gr
Or, T1=h1ρ1gr2cosθ1

T1=0.1×1000×10×r2×1
T1=500r ...(ii)


For Mercury
Depression in level, h2=0.0342 m
(ve sign as height is depressed)
ρ2=13.6gm/cm3=13600 kg/m3
θ2=135
Radius of tube =r

Similarly from Eq (i),
T2=0.0342×13600×10×r2cos135

T2=0.0342×136000×r2×(12)
T2=3264r ...(iii)

T1T2=500 r3264 r
T1T2=0.153

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