Question

A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of the water in the capillary is $5\text{g}$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is

• A. $15\text{g}$
• B. $10\text{g}$
• C. $18\text{g}$
• D. $20\text{g}$

Answer 1

The correct option is B $10\text{g}$

We know that, capillary rise $\left(h\right)$,

$h=\frac{2T\cos \theta }{\rho gr}$

$\Rightarrow \rho h=\frac{2T\cos \theta }{gr}.......\left(1\right)$

Also, mass $\left(m\right)=\rho V$

$\Rightarrow m=\rho hA$

$\Rightarrow m=\frac{2TA\cos \theta }{gr}$ [from Eq. (1)]

For same fluid,

$m\propto \frac{A}{r}\Rightarrow m\propto \frac{\pi r^2}{r}\Rightarrow m\propto r$

So, $\frac{m_1}{m_2}=\frac{r_1}{r_2}$

Substituting the given values we get,

$\frac{5}{m_2}=\frac{r}{2r}\Rightarrow m_2=10\text{g}$

Hence, option (b) is the correct answer.

Why this question? Tip: In this kind of question we should always form a proportion and subtitute the known values to find the unknown data.