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A capillary tube with very thin walls is...

A capillary tube with very thin walls is attached to the beam of a balance which is then equalized. The lower end of the capillry is brought in contact with the surface of water after which an additional load of `P = 0.135 gm` force is needed to regain equilibrium. If the radius of the capillary is `(lambda)/(10)cm` then find `lambda` The surface tension of water is `70 "dyne"//"cm"`. `(g = 9.8 m//s^(2))`

Text Solution

Verified by Experts

The correct Answer is:
`15`
Let the mass of capillary tube only is `'m'` so, that balanced beanm is given by.

Now the end of capillary is brought in contact with the water, so some height is raised in the capillary.
Lets says, our systeam is capillary plus the water inside of height `'h'` The force of surface of tension at the end is being felt by capillary in the downward direction.
At the force of surface tension at the top becomes internal force for are system.
so.
`F + pihgA = ["extra mass" (0.135)] xx g`.
and we know for capillary risen water `rhogh pir^(2) = T xx 2 pir`.
so `2T xx 2pir = (0.135 xx 10^(-3)) xx g`
get `r approx 1.5 mm`.
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