Question

A long cylindrical glass vessel has a pinhole of diameter $0.2mm$ at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water, $T=0.07N{m}^{-1}$, acceleration due to gravity, $g=10m{s}^{-2}$ )

• A. 14 cm
• B. 7cm
• C. 21 cm
• D. 28 cm

Answer 1

Answer: (A)

Given, diameter of a pinhole, $d=0.2mm$
$\therefore$ radius of pinhole, $r=\frac{0.2}{2}=0.1mm=0.1\times 10^{-3}m$
When the hydrostatic pressure is equal to the excess pressure, then water cannot enter the pinhole
Hence, $h\rho g=\frac{2T}{r}$
where, $h$= depth up to which cylinder is immersed.
$\rho =$ density of water
$T=$ surface tension of water
and $r=$ radius of a pinhole
$\therefore h=\frac{2T}{\rho gr}=\frac{2\times 0.07}{10^3\times 10\times 0.1\times 10^{-3}}$
$=0.14m=14cm$
Hence, the depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is $14cm$