Question

When a capillary is immersed in a liquid, then liquid of mass M rises in the capillary tube. If capillary tube of double the radius is taken then the mass of same liquid rising in the tube is?

• A. $2M$
• B. $M/2$
• C. $4M$
• D. None of these

Answer 1

The correct option is A $2M$

$\begin{array}{c}Massofwaterri\sin ginthetubeofradiusrisgivenby,\\ M=\pi r^{2}h\rho \\ Now,\\ surfacetension,\sigma =\frac{h\rho gr}{2}=\frac{h^{\prime }\rho g{r}^{\prime }}{2}\\ where{h}^{\prime }istheheighttowhichwaterrisesinthe\sec ondtubeand{r}^{\prime }itsradius.\\ \sin ce{r}^{\prime }=2r,h^{\prime }=\frac{h}{2}\\ therefore,themassofwaterinthe\sec ondtubeisgivenby,\\ M^{\prime }=\pi r{}^{\prime 2}{h}^{\prime }\rho \\ =\pi {\left(2r\right)}^2\frac{h}{2}\rho =2\pi r^{2}h\rho =2M\end{array}$

Hence,

option $\left(A\right)$ is correct answer.