Physics - Fluid Question with Solution | TestHub

The height of liquid in a capillary tube is given by Jurin's law:

$h=\frac{2T\cos \theta }{r\rho g}$

The mass of the liquid in the capillary tube is:

$m=\pi r^{2}h\rho$

Substituting the expression for $h$ into the mass equation:

$m=\pi r^2\left(\frac{2T\cos \theta }{r\rho g}\right)\rho =\frac{2\pi rT\cos \theta }{g}$

This shows that the mass of the liquid raised is directly proportional to the radius of the capillary tube, i.e., $m\propto r$.

For the new capillary tube, the radius is $r^{\prime }=\frac{r}{5}$.

Therefore, the new mass $m^{\prime }$ will be:

$m^{\prime }=\frac{m}{5}$

Answer: $\frac{\mathrm{m}}{5}$