Two capillary tubes of diameters `3.0 mm` and `6.0 mm` are joined together to form a `U`-tube open at both ends. If the `U`-tube is filled with water, what is the difference in its levels in the two limbs of the tube ? Surface tension of water at the temperature of the experiment is `7.3xx10^(2)N//m`. Take the angie of contact to be zero and density of water to be `10^(3)kg//m^(3)`(`g=9.8m//s^(2)`)

Options

A. `5mm`
B. `10mm`
C. `15mm`
D. `20mm`

Explanation

For the first bore, pressure difference (between the concave and convex side)
`=(2xx7.3xx10^(-2))/(3xx10^(-3))=48.7Pa`. Similarly for the second bore, pressure difference `=97.3 Pa`.
Consequently , the level difference in the two bores is `[(48.7)/(10^(3)xx9.8)]m=5.0mm`. The level in the narrower bore is higher. (Note, for zero angle of contace, the radius of the meniscus equals radius of the bore. The concave side of the surface in each bore is at `1 "atm"`).