Three liquids of densities `rho_(1), rho_(2)` and `rho_(3)` (with `rho_(1) gt rho_(2) gt rho_(3)`), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact `theta_(1), theta_(2)` and `theta_(3)` obey

Options

A. `(pi)/(2)gt theta_(1) gt theta_(2) gt theta_(3) ge 0`
B. `0 le theta_(1) lt theta_(2) lt theta_(3) lt (pi)/(2)`
C. `(pi)/(2) lt theta_(1) lt theta_(2) lt theta_(3) lt pi`
D. `pi gt theta_(1) gt theta_(2) gt theta_(3) gt (pi)/(2)`

Answer

B

Explanation

Capillary rise, `h= (2T cos theta)/(r rho g)`
For given value of T and r, `h prop (cos theta)/(rho)`
Also, `h_(1) =h_(2) or, (cos theta_(1))/(rho_(1)) = (cos theta_(2))/(rho_(2)) = (cos theta_(3))/(rho_(3))`
Since, `rho_(1) gt rho_(2) gt rho_(3)`, so `cos theta_(1) gt cos theta_(2) gt cos theta_(3)`
For `0 le theta lt (pi)/(2), theta_(1) lt theta_(2) lt theta_(3)`
Hence, `theta le theta_(1) lt theta_(2) lt theta_(3) lt (pi)/(2)`