Question

Can somebody explain me the meaning of this question .

A glass rod of diameter d=2mm is inserted symmetrically into a glass capillary tube of radius r=2mm . Then the whole arrangement is vertically dipped into liquid having surface tension 0.072 N/m. The height to which the liquid will rise on capillary is ?
Assume contact angle to be zero and length of capillary tube to be long enough .

Answer 1

It means that the separation of the rod from the inner wall of the tube is everywhere the same or in other words the rod placed in the center of the tube.

Answer 2

Thank you . :)
But , I am still not able to solve it , any idea how to do so ?

Answer 3

@Dexter810

I can help. The force along the line of contact of a liquid and a solid due to surface tension is equal to the length of the line of contact times the surface tension. So for a circular container with a radius of r the force is
\[2\pi \sigma r\]
for a square column it would be
\[4a \sigma\]
where a is the length of the side so the force in a annulus formed by a rod or radius r1 in a tube with an internal radius of r2 is
\[2\pi (r _{2}+r _{1}) \sigma \]. Got that?

Now for a liquid climbing up a narrow space to due capillary action the pressure is greater on the air side than the liquid side that's why it bows in. To establish equilibrium the total force acting on the surface of the liquid must balance the force of the air pressure pushing down. The surface tension force resists the force of the air pressure keeping the surface in place. But the surface tension force is equal to the weight of the height of the liquid column that it is supporting. For your case the length of contact of the surface tension force is \[2\pi(r _{2}+r _{1}) \] so the total supporting force is st*2pi(r1+r2)

this must equal the weight of the liquid column which is \[ mgh= h*(area .of .the. liquid.surface)*\rho*g =h g \rho\pi(r _{2}^{2} -r _{1}^2) \]] where rho is the denisty of the liquid and h is the heigth of the liquid column. Therefore this must equal \[2 \pi (r _{2}+r _{1} ) \sigma \] remember?

Can you take it from here?