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Question

If a 5 cm long capillary tube with 0.2 mm internal diameter open at both ends is slightly dipped in water having surface tension 75 dyne/cm. What will be the rise of water in capillary (Take g=1000 cm/s2)

A
15 cm
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B
5 cm
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C
10 cm
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D
20 cm
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Solution

The correct option is B 5 cm
Given that
Surface tension, T=75 dyne/cm
Radius, (r)=0.22 mm=0.1 m=0.01 cm
Density of water, ρ=1 gm/cm3
Angle of contact, θ=0o
Let h be the height to which water will rises in the capillary tube. Then
h=2Tcosθrρg=2×75×cos00.01×1×1000=15 cm
But legth of capilalry tube is 5 cm
Because the tube is of insufficient length therefore the water will rise upto the upper end of the tube.
h=5 cm
Why this question?
Tips: If length of tube < height of capillary rise, then the total rise of water in capillary will be equal to the length of the tube but angle of contact will change.

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