Question

A capillary tube of radius $r$ is immersed in water and water rises to a height of $h$. Mass of water in the capillary tube is $5\times {10}^{-3}kg$. The same capillary tube is now immersed in a liquid whose surface tension is $\sqrt{2}$ times the surface tension of water. The angle of contact between the capillary tube and this liquid is ${45}^o$. The mass of liquid which rises into the capillary tube now is (in kg):

• A. $5\times {10}^{-3}$
• B. $2.5\times {10}^{-3}$
• C. $5\sqrt{2}\times {10}^{-3}$
• D. $3.5\times {10}^{-3}$

Answer 1

Answer: (A)

$5\times {10}^{-3}$

Since the force on liquid is proportional to $Scos\left(\theta \right)$, in the latter case, force will be $\sqrt{2}cos\left(\frac{\pi }{4}\right)=1$ times the force in first case. Hence, since the same force is applied, mass of water rising in the tube will be same.