Question

A capillary tube of radius $r$ is immersed in a liquid and mass of liquid, which rises up in it is $M$. If the radius of tube is doubled, then the mass of liquid which will rise in capillary tube will be

• A. 2 M
• B. M
• C. M/2
• D. M/4

Answer 1

Answer: (A)

$M=\rho v$
$\Rightarrow $ Mass $\propto$ volume of tube
Mass $\propto$ height $\times$ Area
$\Rightarrow $ Mass $\propto \frac{1}{r} \times r^{2}$
Mass $\propto r$
$\because$ If radius doubles, mass of liquid that rises up also doubles
Area $\propto r^{2}$
Height $\propto \frac{1}{r}$
$\left(h=\frac{2 S}{r g h}\right)$
Where $r =$ radius of cube