Three liquids of densities `rho_(1),rho_(2)andrho_(3)(rho_(1)gtrho_(2)gtrho_(3))` having same value of surface tension T,rise to the same heitht in three identical capillaries . The following relation is remain true ?

Options

A. `(pi)/(2)lttheta_(1)lttheta_(2)lttheta_(3)ltpi`
B. `pigttheta_(1)gttheta_(2)gttheta_(3)gt(pi)/(2)`
C. `(pi)/(2)gttheta_(1)gttheta_(2)gttheta_(3)gt0`
D. `0letheta_(1)lttheta_(2)lttheta_(3)lt(pi)/(2)`

Answer

d

Explanation

When a capillary is placed vertically in aliquid the rise of liquid,
`h=(2Tcostheta)/(lrhog)`
here h,2,T, and g are constant
`therefore(costheta)/(rho)=` constant
`therefore(costheta_(1))/(rho_1)=(costheta_(2))/(rho_(2))=(costheta_(3))/(rho_(3))`
but `rho_(1)gtrho_(2)gtrho_(3)`
`thereforecostheta_(1)gtcostheta_(2)gtcostheta_(3)`
`thereforetheta_(1)lttheta_(2)lttheta_(3)` [cos is decreasing function in first phase] Water rise in all three capillaries , so angle is acute angle ,
`therefore0letheta_(1)lttheta_(2)lttheta_(3)lt(pi)/(2)`