Question

If $M$ is the mass of water rises in a capillary tube of radius $r$, then what will be the mass of water which will rise in a capillary tube of same material having radius $2r$?

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

Answer 1

The correct option is A $2M$

Height of liquid rise in capillary tube,
$h=\frac{2T\cos {\theta }_C}{\rho rg}$
Since fluid and material of the tube remains same,
$\Rightarrow h\propto \frac{1}{r}$
So, when radius is doubled, height becomes half.
$\therefore h^{\prime }=h/2$
Now, density $\left(\rho \right)=\frac{\text{mass}\left(M\right)}{\text{volume}\text{(V)}}$
$\Rightarrow M=\rho \times \pi r^{2}h$
$\therefore M^{\prime }=\rho \pi r^{\prime 2}{h}^{\prime }$
$\therefore \frac{M^{\prime }}{M}=\frac{r^{\prime 2}{h}^{\prime }}{r^{2}h}=\frac{\left(2r{)}^2\right(h/2)}{r^{2}h}=2$
$\Rightarrow M^{\prime }=2M$