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

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

MHT CETMHT CET 2021

Solution:

Given, $h_1=3.2 \,cm$
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}=4.5 cm$