Question

A long cylindrical glass vessel has a pinhole of diameter $0.2\, mm$ 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, $T=0.07 \,Nm ^{-1}$, acceleration due to gravity, $g=10 \,ms ^{-2}$ )

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

Answer 1

Answer: (A)

14 cm

Answer 2

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