Question

If $M$ is the mass of water that rises in a capillary tube of radius $r$, then mass of water which will rise in a capillary tube (of same material) of radius $2r$ is

• A. $2M$
• B. $4M$
• C. $M/2$
• D. $M$

Answer 1

The correct option is A $2M$

Mass of water that rises in first capillary $=M$
Radius of first capillary $=r$
Radius of second capillary $=2r$

Let Mass of water that rises in second capillary $=M^{\prime }$


Applying capillary rise equation:
$h=\frac{2T\cos \theta }{\rho gr}...\left(i\right)$

mass $M=\rho V$ where ($V$ is volume)
$\therefore M=\rho \times h\times A=\rho h\pi r^2...\left(ii\right)$

From Eq. $\left(i\right)\&\left(ii\right)$,
$M=\rho \pi r^2\times \frac{2T\cos \theta }{\rho gr}=\frac{2\pi Tr\cos \theta }{g}...\left(iii\right)$
$\because M\propto r$
[$T$ and $\theta$ will be same as fluid is same]
$\Rightarrow M^{\prime }\propto \left(2r\right)$
$\frac{M^{\prime }}{M}=\frac{2r}{r}$
$\therefore M^{\prime }=2M$
Hence, $2M$ amount of mass will rise in capillary tube of radius $2r$.