question_answer

Water of density p in a clean aquarium forms a meniscus, as illustrated in the figure. Calculate the difference in height h between the centre and the edge of the meniscus. The surface tension of water is\[\gamma \].                

A) \[\sqrt{\frac{2\gamma }{\rho g}}\]

B) \[\sqrt{\frac{\gamma }{\rho g}}\]

C) \[\frac{1}{2}\sqrt{\frac{\gamma }{\rho g}}\]

D) \[2\sqrt{\frac{\gamma }{\rho g}}\]

Correct Answer: A

Solution :

[a]    Balancing forces in horizontal direction \[\left( {{p}_{0}}-\rho g\frac{h}{2} \right)\ell h=\gamma \ell ={{p}_{0}}\ell h\Rightarrow h=\sqrt{\frac{2\gamma }{\rho g}}\]