Question

A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. Mass of water in the capillary tube is $m$. If the radius of the tube is doubled, mass of water that will rise in the capillary tube will now be

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

Answer 1

The correct option is B $2m$

We have $m=\pi r^{2}h$
when radius of tube is doubled ($r^{\prime }=2r$) water will rise to a height $h^{\prime }=\frac{h}{2}$
Hence,
$m=\pi {r^{\prime }}^{2}h=\pi {\left(2r\right)}^2\left(\frac{h}{2}\right)=2\pi rh=2m$