A vertical capillary tube with inside diameter `0.50 mm` is submerged into water so that the length of its part emerging outside the water surface is equal to `25 mm`. Find the radius of curvature of the meniscus. Surface tension of water is `73xx10^(-3)N//m`.

Options

A. `R=0.6m`
B. `R=6mm`
C. `R=0.6mm`
D. `R=0.6Km`

Answer

C

Explanation

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`
`becauseh=(2xx73xx10^(-3))/(0.25xx10^(-3)xx10^(3)xx9.8)=59xx10^(-3)m=59mm`
Now `hgth^(')`, i.e., length is outside water surface Therefore, radius of meniscus `gt` radius of capillary `r`.
If `R` is the radius of meniscus then we have
`(2T)/(R)=h^(')rhog` or `R=(2T)/(h^(')rhog)`
Here `h^(1)=25mm=25xx10^(-3)m`
`becauseR=(2xx73xx10^(-3))/(25xx10^(-3)xx9.8)=0.6xx10^(-3)m`