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Question

A glass capillary tube of inner diameter 0.28 mm is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that water level in the tube is same as that in the vessel (in N/m2) is
(Surface tension of water =0.07 N/m and atmospheric pressure =105 N/m2)
  1. 103
  2. 99×103
  3. 100×103
  4. 101×103


Solution

The correct option is D 101×103
Diameter of tubed=0.28 mm=0.28×103 m
r=0.14×103 m
Surface tension, T=0.07 N/m
Atm. pressure = 105 N/m2
Now, pressure due to h height column of water in tube =ρgh
And by formula of capillary rise, h=2Tcosθrρg
For water θ=0
So, we get
P=ρgh=2Tr=2×0.070.14×103=103 N/m2
So, pressure due to height h is =103 N/m2
Total pressure required to be applied =P+ Atmospheric pressure
=103+105
=101×103 N/m2 

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