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 radius $2r$ is

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

Answer 1

The correct option is D $2M$

We have,
Rise in capillary height $h=\frac{2T\cos \theta }{r\rho g}$

Mass of the water in the capillary
$m=\rho V=\rho \times \pi r^{2}h$
$m=\rho \times \pi r^2\times \frac{2T\cos \theta }{r\rho g}$
$\Rightarrow m\propto r$
$\therefore \frac{m_1}{m_2}=\frac{r_1}{r_2}$
$\Rightarrow \frac{m_1}{m_2}=\frac{r}{2r}$
$M_2=2M_1=2M$
Hence option $\left(D\right)$ is correct.