A glass rod of radius `r_(1)` is inserted symmetrically into a vertical capillary tube of radius `r_(2)` such that their lower ends are at the same level. The arrangement is now dipped in water. The height to which water will rise into the tube will be (`sigma =` surface tension of water, `rho = ` density of water)

Options

A. `(2sigma)/((r_(2)-r_(1))rhog)`
B. `sigma/((r_(2)-r_(1))rhog)`
C. `(2sigma)/((r_(2)+r_(1))rhog)`
D. `(2sigma)/((r_(2)^(2)+r_(1)^(2))rhog)`

Answer

A

Explanation

Total upward force due to surface tension `=sigma(2r_(1)+2pi_(2))`. This supports the weight of the liquid column of height `h`. Weight of liquid column` =[pir_(2)^(2)-pir_(1)^(2)]rhog`
Equating we get `hpi(r_(2)+r_(1))(r_(2)-r_(1))rho=2pisigma(r_(1)+r_(2))`