Question

Water rises to a height $h$ in a capillary tube of area of cross-section $a$. To what height will water rise in a capillary tube of radius of cross-section 4a?

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

Answer 1

The correct option is B

$\frac{h}{2}$

Area of cross-section, $a=\pi r^2\Rightarrow r=\sqrt{\frac{a}{\pi }}$
Now, height rise in a capillary tube is given by $h=\frac{2\sigma cos\theta }{r\rho g}=\frac{2\sqrt{\pi }\sigma cos\theta }{\sqrt{a}\rho g}$
As $h\propto \frac{1}{\sqrt{a}}$, if $a$ is increased 4 times, $h$ will decrease by a factor of 2.
Hence, the correct choice is (b).