1)

A glass capillary tube is of the shape of a truncated cone with an apex angle  α  so that its two ends have cross-sections of different radii. When dipped in water vertically, water rises in its height h, where the radius of its cross-section in b. If the4 surface tension of water is S.  its density is ρ, and its contact angle with glass is θ, the value of h will be (g is the acceleration due to gravity)

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A) 2Sbρgcos(θα)

B) 2Sbρgcos(θ+α)

C) 2Sbρgcos(θα/2)

D) 2Sbρgcos(θ+α/2)

Answer:

Option D

Explanation:

Using geometry 

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bR=cos(θ+α2)

   R=bcos(θ+α2)

  Using pressure  equation along the path MNTK

p02SR+hρg=p0

 Substituting the value of R , we get 

           h=2SRρg

         =2Sbρgcos(θ+α2)