Water rises in a capillarity tube to a height 2.0 cm. if the tube is inclined at an angle of 60° with the vertical, what will be the length of the water column within the tube?
A
4 cms
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B
cms
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C
1 cm
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D
None of these
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Solution
The correct option is A
4 cms
When the tube is vertical, the column of liquid in the tube is kept up only by the force of adhesion between the tube and the water. where FA is the adhesive force FA=2πrScosθ For equilibrium Mg=2πrScosθ ⇒πr2h1ρg=2πrScosθ ⇒h1=2πrScosθπr2ρg=2Scosθrρg When it is inclined
Due to equilibrium N=Mgsin60∘ ⇒N=πr2h2ρgsin60∘=πr2h2ρg√32.......(1) FA=Mgcos60∘ FA=πr2h2ρg12 ⇒h2=2πrScosθπr2ρg×2 =[2scosθrρg]×2 =4cm