Question

Water rises upto a height $h$ in a capillary tube of certain diameter. This capillary tube is replaced by a similar tube of half the diameter. Now the water will rise to the height of:

• A. $4h$
• B. $3h$
• C. $2h$
• D. $h$

Answer 1

The correct option is C $2h$

The height $h$ to which the liquid rises in a capillary tube is given by
$h=\frac{2T\cos \theta }{r\rho g}$
$\Rightarrow hr=$ constant
Where,
$h=$ height upto which water rises
$r=$ radius of capillary tube
Let $h^{\prime }$ be the new height
Given: $r^{\prime }=\frac{r}{2}$
$\therefore h^{\prime }{r}^{\prime }=hr$
$\Rightarrow h^{\prime }=\frac{hr}{r^{\prime }}=\frac{hr}{r/2}=2h$
$\Rightarrow h^{\prime }=2h$