A glass capillary tube of inner diameter 0.28 $\mathrm{mm}$ is lowered vertically into water in a vessel.…

A glass capillary tube of inner diameter 0.28 $\mathrm{mm}$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that water level in the tube is same as that in the vessel (in $\mathrm{N} / \mathrm{m}^2$ ) is Surface tension of water $=0.07 \mathrm{~N} / \mathrm{m}$ Atmospheric pressure $=10^5 \mathrm{~N} / \mathrm{m}^2$
  1. $10^3$
  2. $99 \times 10^3$
  3. $100 \times 10^3$
  4. $101 \times 10^3$

Solution

Diameter $d=0.28 \mathrm{~mm}=0.28 \times 10^{-3} \mathrm{~m}$ Radius $r=\frac{d}{2}=0.14 \times 10^{-3} \mathrm{~m}$ Surface tension $T=0.07 \mathrm{~N} / \mathrm{m}$ $T=\frac{r h d g}{2 \cos \theta}$ For water $\theta=0^{\circ}$ $\begin{aligned} \therefore \quad \cos \theta & =1 \\ T & =\frac{r(h d g)}{2}=\frac{r P}{2} \end{aligned}$ $\begin{aligned} & \qquad \begin{aligned} P & =\frac{2 T}{r}=\frac{2 \times 0.07}{0.14 \times 10^{-3}} \\ & =1 \times 10^3 \mathrm{~N} / \mathrm{m}^2 \\ \text { Total pressure } & =P+\text { atmospheric pressure } \\ & =1 \times 10^3+10^5 \\ & =1 \times 10^3+100 \times 10^3 \\ & =101 \times 10^3 \mathrm{~N} / \mathrm{m}^2\end{aligned}\end{aligned}$ .

Asked in: MHT CET Full Test 12

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