Question

A capillary tube of radius '$r$' is immersed in water and water rises in it to a height $H$. Mass of water in the capillary tube is $m$. $(r<<H)$ If the Capillary of radius $2r$ is taken and dipped in water, the mass of water that will rise in the capillary tube will be:

• A. $m$
• B. $2m$
• C. $m/2$
• D. $4m$

Answer 1

The correct option is B $2m$

The height to which the liquid rises in a capillary=$h=\frac{2Tcos\theta }{\rho gr}$

Hence $h\propto \frac{1}{r}$

$⟹\frac{h_2}{h_1}=\frac{r_1}{r_2}=\frac{1}{2}$

Hence the ratio of masses=$\frac{m^{\prime }}{m}=\frac{\rho \times \pi r_2^2{h}_2}{\rho \times \pi r_1^2{h}_1}=2$

$⟹m^{\prime }=2m$