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 $M$. If the radius of the tube is doubled, mass of water that will rise in the capillary tube will now be :

• A. M
• B. 2 M
• C. M/2
• D. 4 M

Answer 1

Answer: (A)

M

Answer 2

Mass of water in capillary rise $=$ Ahp
$A =$ area of cross-section,
$h =$ height, $\rho=$ density
$\Rightarrow m =\left(\pi r ^{2}\right) h \rho=\pi r ^{2} \times \frac{2 \sigma \cos \theta}{ r \rho g}$
$\Rightarrow m \propto r$
$\therefore$ Doubling radius
$\Rightarrow$ mass will also get doubled
$m '=2 M$