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A glass capillary tube is of the shape o...

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

A

(a) `(2S)/(brhog)cos(theta-alpha)`

B

(b) `(2S)/(brhog)cos(theta+alpha)`

C

(c) `(2S)/(brhog)cos(theta-alpha//2)`

D

(d) `(2S)/(brhog)cos(theta+a//2)`

Text Solution

Verified by Experts

The correct Answer is:
D

In `DeltaPCM cos (theta-alpha/2)=b/R` …(i)
Also `(P_0-(2S)/(R))+hrhog=P_0`
`h=(2S)/(Rrhog)=(2S)/(brhog)cos(theta+alpha//2)`
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