Question

Water rises to height $3.2cm$ in glass capillary tube. Find the height to which same water rises in another capillary having half the area of cross-section.

• A. $4.5cm$
• B. $5.0cm$
• C. $5.4cm$
• D. $6.2cm$

Answer 1

Answer: (A)

Given, $h_1=3.2cm$
As per question,
$\frac{1}{2}\text{ (area of first capillary) }=\text{ Area of second capillary }$
$\Rightarrow \frac{1}{2}\times \pi r_1^2=\pi r_2^2\Rightarrow r_1=\sqrt{2}{r}_2$
For same fluid,
$h_1{r}_1=h_2{r}_2$
$\Rightarrow h_2=\frac{h_1{r}_1}{r_2}=\frac{3.2\times \sqrt{2}{r}_2}{r_2}=4.5cm$