Question

A vessel, whose bottom has round holes with diameter of $ 1\,mm $ is filled with water. Assuming that surface tension acts only at holes. Then, the maximum height to which the water can be filled in vessel without leakage is (surface tension of water is $ 75\times 10^{-3}\,N/m$ and $g=10\, m/s^{2}$)

• A. 3 cm
• B. 0.3 cm
• C. 3 mm
• D. 3 m

Answer 1

Answer: (A)

For no leakage, $h \rho g=\frac{2 T}{R}$
$\Rightarrow T=\frac{R h \rho g}{2}$
$\Rightarrow h=\frac{2 T}{R \rho g}$
Given, $T=75 \times 10^{-3} N / m,$
$g=10\, m / s ^{2},$
$R=0.5 \times 10^{-3} m$
$h=\frac{2 \times 75 \times 10^{-3}}{\left(0.5 \times 10^{-3}\right)(1000) 10}$
$\Rightarrow h=30 \times 10^{-3} \times 100\, cm$
$=3\, cm$