A glass rod of diameter `d_(1)=1.5 mm` in inserted symmetrically into a glass capillary with inside diameter `d_(2)=2.0` mm. Then the whole arrangement is vertically oriented and brought in contact with the surface of water. To what height will the liquid rise in the capillary?
Surface tension of water `=73xx10^(-3)N//m`

Explanation

Suppose the liquid rises to a height `h` . Then the total energy of the liquid in the capillary is
`E (h) = (pi)/(4) (d_2^2 - d_1^2) h xx rho g xx (h)/(2) - pi (d_2 - d_1) alpha h`
Minimising `E` we get
`h = (4 alpha)/(rho g(d_2 - d_1)) = 6 cm`.