If a `5 cm` long capillary tube with `0.1 mm` internal diameter, open at both ends, is slightly dipped in water having surface tension `75 dyn//cm`, state whether: water will rise halfway in the capillary, (ii) water will rig up to the upper end of capillary, (iii) water will overflow out of the upper end of capillary. Explain your answer.

Explanation

Given that surface tension of water
`T=75"dyne"//cm`
Radius `r=0.1/2mm=0.05mm=0.05cm`
density `rho=1gm//cm^(3)` angle of contact `theta=0^@`
Let `h` be the height to which water rise in the capillary tube.
Then
`h=(2Tcostheta)/(rrhog)=(2x75xxcos0^@)/(0.005xx1xx981)cm=30.58cm`
but length of capillary tube `h'=5cm`
a. because `hgth'//2` therefore the first possibility does not exit.
b.Because the is of insufficient length, therefore the water will rise up to the upper end of the tube.
c. The water will not overflow out of the upper end of the capillary. It will rise only up to the upper end of the capillary.
The liquid meniscus will adjust its radius of curvature `R'` in such a way
`R'h'=[hR=(2T)/(rhog)= "constant"]`
where `R` is the radius of curvature that the liquid meniscus would posses if the capillary tube were of sufficient length
`R'=(Rh)/h=(rh)/h'[R=r/(costheta)=r/(cos0^@)=r]`
`=(0.005xx30.58)/5=0.0306cm`