Question

Water rises up to a height $h_1$ in a capillary tube of radius $r$. the mass of the water lifted in the capillary tube is $M$. if the radius of the capillary tube is doubled, the mass of water that will rise in the capillary tube will be

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

Answer 1

The correct option is B $2M$

Capillary rise, $h=\frac{2r\cos \theta }{\rho gr}$ where $\rho$ (density) $\propto M$

Tube radius $=r,$ Angle of contact $=\theta$

$\therefore$ Capillary mass $M\propto$ radius of tube $r$

$\Rightarrow$ On doubling $r$ to $2r$

$\Rightarrow$ $M$ to $2M$