Q47 / 50 · Manipal (MET) 2023 · Physics
The lower end of a capillary tube is dipped into water and it is seen that water rises through 7.5 cm in the capillary. Given, surface tension of water is $7.5 \times 10^{-2} \mathrm{Nm}^{-1}$ and angle of contact between water and glass capillary tube is zero.
What will be the diameter (in mm ) of the capillary tube? (given, $g=10 \mathrm{~ms}^{-2}$ )
Correct answer: 0.4
Solution
Given, $h=7.5 \mathrm{~cm}=7.5 \times 10^{-2} \mathrm{~m}$
$\begin{aligned}& S=7.5 \times 10^{-2} \mathrm{Nm}^{-1} \\
& \theta=\sigma^{\circ}, r=?\end{aligned}$
As, $h=\frac{2 S \cos \theta}{r \rho g} \Rightarrow 2 r=\frac{4 S \cos \theta}{h \rho g}$
$=\frac{4 \times 7.5 \times 10^{-2} \times \cos 0^{\circ}}{7.5 \times 10^{-2} \times 10^3 \times 10}=4 \times 10^{-4}=0.4 \mathrm{~mm}$
Hence, the correct answer is 0.4.