Question

Three liquids of densities ${\rho }_1$ , ${\rho }_2$, and ${\rho }_3$
$(With{\rho }_1>{\rho }_2>{\rho }_3)$, having the same value of surface tension T,rise to the same height in three identical capillarise. The angles of contact ${\theta }_1$, ${\theta }_2$, and ${\theta }_3$ obey:-

• A. $\frac{\pi }{2}<{\theta }_1<{\theta }_2<{\theta }_3<\pi$
• B. $\pi >{\theta }_1>{\theta }_2>{\theta }_3>\frac{\pi }{2}$
• C. $\frac{\pi }{2}>{\theta }_1>{\theta }_2>{\theta }_3>0$
• D. $0\le {\theta }_1<{\theta }_2<{\theta }_3<\frac{\pi }{2}$

Answer 1

The correct option is D $0\le {\theta }_1<{\theta }_2<{\theta }_3<\frac{\pi }{2}$

Rise of a liquid in a capillary tube is $h=\frac{2T\cos \theta }{r\rho g}$

For equal height and surface tension, $\cos \theta \alpha \rho$, range $(0\le \theta <\frac{\pi }{2})$

Hence, if density increase, $\theta$will decrease.

${\rho }_1>{\rho }_2>{\rho }_3$ , $0\le {\theta }_1<{\theta }_2<{\theta }_3<\frac{\pi }{2}$