A vessel whose , bottom has round holes with diameter `0.1 mm`, is filled with water. The maximum height up to which water can be filled without leakage is

Options

A. `100 cm`
B. `75 cm`
C. `50 cm`
D. `30 cm`

Answer

D

Explanation

For equilibrium
Total force by suface tension
`=` Weight of the water in tube
`implies pixxDxx` surface tension (circumference)
`=pi(D/2)^(2)xxhxx"density"xxg` (cross section)
where `D` (diameter) `=0.1mm=0.01cm`
Density of water `=1xx10^(-3)g//cm^(3)`
`implies pixx(0.01)xx75xx10^(-3)`

`=pixx(0.01/2)^(2)xxhxx1xx10^(-3)xx1000`
`=h=(0.75xx0.01xx4)/(0.01xx0.01)=0.3m=30cm`