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A capillary tube of inside diameter 1mm ...

A capillary tube of inside diameter 1mm is dipped vertically into water, so that the length of its part protruding over the water surface is 20mm.What is the radius of curvatur of the meniscus ? Surface tension of water is `72 xx 10^(-3) N//m`.

Text Solution

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In the capillary tube, the water should rise to a height
`h=(2T)/(rrhog)`
Here
`T=73xx10^(-3)N.m`
`r=(0.50mm)/2=0.25xx10^(-3)m`
`rho=10^(3)kg//m^(3)`
`:. H=(2xx73xx10^(-3))/(0.25xx10^(-3)xx10^(3)xx9.8)=59xx10^(-3)m=59m`
Now `hgth'`, i.e., length is outside water surrface
Therefore radius of meniscusgtradius of capillary `r`.
If `R` is the radius of meniscus, then we have
`(2T)/R=h'rhog`
or `R=(2T)/(h'rhog)`
Here `h'=25mm=25xx10^(-3)m`
`:.R=(2xx73xx10^(-3))/(25xx10^(-3)xx10^(3)xx9.8)=0.6xx10^(-3)m=0.6m`
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