Question

A capillary tube of radius of cross section r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is m. Another capillary is also immersed in water. The mass of water that rises in this capillary is $\frac{m}{2}$. The radius of cross section of this capillary is

• A. $2r$
• B. $r$
• C. $\frac{r}{2}$
• D. $\frac{r}{4}$

Answer 1

The correct option is C $\frac{r}{2}$

$h=\frac{2Tcos\theta }{r\rho g}=\frac{2TR}{\rho g}$
$m=\pi r^{2}h\rho$ and $h=\frac{2TR}{\rho g}$
$\therefore \frac{m}{2}=\pi r^2{h}^{\prime }$ and $h=\frac{2T{R}^{\prime }}{\rho g}$
$\frac{r^2}{2}\times \frac{2T}{r\rho g}=r^{{}^{\prime }2}\frac{2T}{r^{\prime }\rho g}\Rightarrow r^{\prime }=\frac{r}{2}$.