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

Three liquids of densities rho_(1),rho_(2)andrho_(3)(rho_(1)gtrho_(2)g

1.	Three liquids of densities rho_(1),rho_(2)andrho_(3)(rho_(1)gtrho_(2)gtrho_(3)) having samevalue of surface tension T,rise to the same heitht in three identical capillaries . The following relation is remain true ?
Answer» `(pi)/(2)lttheta_(1)lttheta_(2)lttheta_(3)ltpi` `pigttheta_(1)gttheta_(2)gttheta_(3)gt(pi)/(2)` `(pi)/(2)gttheta_(1)gttheta_(2)gttheta_(3)gt0` `0letheta_(1)lttheta_(2)lttheta_(3)lt(pi)/(2)` Solution :When a capillaryis placedvertically 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)`