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  • A  - diameter tube was placed in a sample of waters ot <img alt="20^{\circ} \math

A 0.2 \mathrm{~mm} - diameter tube was placed in a sample of waters ot 20^{\circ} \mathrm{C}. As a result of capillary action, the water rose inside the tube to a height of 11.40 \mathrm{~cm}. Determine the exact diameter of the tube.

\begin{aligned}\gamma\left(\mathrm{H}_2 \mathrm{O}\right)=72.75 \times 10^{-3} \mathrm{~N} / \mathrm{m},\mathrm {d}\left(\mathrm{H}_2 \mathrm{O}\right)=0.998 \text { glam } 2.608 \times 10^4 \mathrm{~m} \text { (d) } 7.208 \times 10^4 \mathrm{~m}\end{aligned}
 

Option: 1

2.608 \times 10^{-4} \mathrm{~m}


Option: 2

2.602 \times 10^{-2} \mathrm{~m}


Option: 3

2.608 \times 10^4 \mathrm{~m}


Option: 4

7.208 \times 10^4 \mathrm{~m}


Answers (1)

best_answer

Plan: force due to surface tension =2 \pi \mathrm{nr} and force which holds liquid at a height \mathrm{h=mg}.
whore \mathrm{m=v d=\pi r^2 n d, \pi r^2 h} is the volume and d is the density

\begin{aligned} &\mathrm{ \therefore 2 \pi r r=\pi^2 n d g ; r=\frac{2 r}{h d g}} \\ & \mathrm{r}=2 \times 72.75 \times 10^{-3} \mathrm{~N} / \mathrm{m}=1.304 \times 10^{-4} \mathrm{~m} \\ &\text { Hence, diameter } =2 \times 1.304 \times 10^{-4} \mathrm{~m} \\ & =2.608 \times 10^{-4} \mathrm{~m}\\ \end{aligned}
 

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avinash.dongre

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