Question

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of water in the capillary tube is $10$g. Another capillary tube of radius $\frac{3}{2}$r is immersed in water. The mass of water that will rise in this tube will be.

• A. $20$g
• B. $15$g
• C. $5$g
• D. $10$g

Answer 1

The correct option is B $15$g

The height of capillary is given by
$h=\frac{2s\cos \theta }{r\rho g}$

The mass of water in the tube will be
$m=V\rho =\pi r^{2}h\rho$
$\pi r^2\frac{2s\cos \theta }{r\rho g}\times \rho$
$\Rightarrow m=\frac{2\pi rs\cos \theta }{g}$

So, $m\propto r$
$\therefore \frac{m_1}{m_2}=\frac{r_1}{r_2}\Rightarrow \frac{10}{m_2}=\frac{I}{\frac{3}{2}r}$
$\Rightarrow m_2=10\times \frac{3}{2}=15$g.