JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Fluid Mechanics

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 it to a height

h

, where the radius of its cross section is

b

. If the 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)

Answer: (D)

Solution

For a conical capillary, the meniscus makes an angle with the slanted wall. The effective contact angle with the vertical is

θ + α /2

.

Balancing forces: upward surface tension force = weight of liquid column.

2 π b S cos (θ + α /2) = π b^{2} h ρ g

.

Solving for

h

h = \frac{2 S}{b ρ g} cos (θ + α /2)

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option