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. `(2sigma)/((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 dur to surface tension `=sigma(2pir_(1)+2pir_(2))` This supports the weight of the liquid column of height h. Weight of liquid column liquid column of height h. Weight of liquid column
`=h=[pir_(2)^(2)+2pir_(2))]rhog` Equating,
We get `hpi(r_(2)+r_(1))(r_(2)-r_(1))rhog=2pisigma(r_(1)+r_(2))`
or `h(r_(2)-r_(1))rhog=2sigma` or `h=(2sigma)/((r_(2)-r_(1))rhog)`