Two different vertical positions (a) & (b) of a capillary tube are shown in figure with the lower end inside water. For position (a), contact angle is 45∘ & water rises to height h above the surface of water while for position (b) height of the tube outside water is kept insufficient & equal to h2 then find the new contact angle (in degrees)

h=2Tcos45∘rρg..........(i) h2=2Tcosθrρg..........(ii) (i)&(ii)⇒cosθ=12⇒θ=60∘

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Two different vertical positions (a) & (b) of a capillary tube are shown in figure with the lower end inside water. For position (a), contact angle is $45^{\circ}$ & water rises to height h above the surface of water while for position (b) height of the tube outside water is kept insufficient & equal to $\frac{h}{\sqrt{2}}$ then find the new contact angle (in degrees)

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answer is 60.

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Detailed Solution

$h = \frac{2 T \cos 45^{\circ}}{r ρ g} .......... (i) \frac{h}{\sqrt{2}} = \frac{2 T \cos θ}{r ρ g} .......... (i i) (i) & (i i) \Rightarrow \cos θ = \frac{1}{2} \Rightarrow θ = 60^{\circ}$

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