A vessel has a small circular hole at its bottom. Water can be filled to a height of 7 cm without leaking out (g = 10 m/s², surface tension of water = 0.07 N/m). The radius of the hole is closest to:

2 mm
0.2 mm
0.1 mm
0.4 mm

Correct answer: 0.2 mm

Solution

The surface-tension force on the meniscus at the hole can support a pressure 2S/r. Leakage starts when hydrostatic pressure rho*g*h reaches this: rho*g*h = 2S/r. So r = 2S/(rho*g*h) = 2*0.07/(1000*10*0.07) = 0.14/700 = 2e-4 m = 0.2 mm.

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