Question

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

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

Answer 1

The correct option is C $2h$

Given,

Height in capillary $h_1$

Diameter of capillary $d_1$

We know that,

$h\times \frac{1}{r}$ [where r is the radius of capillary ]

Now the capillary is replaced by half the diameter.

i.e.

$\begin{array}{c}{d}_2=\frac{d_1}{2}\\ \therefore \frac{h_1}{h_2}=\frac{r_1}{r_2}=\frac{d_1\times 2}{2\times d_2}=2\\ \Rightarrow h_2=2h_1\end{array}$

$\therefore$ the rise in the capillary is $2h$.

Hence,

Option $C$ is correct.