A long cylindrical glass vessel has a small hole of radius 'r' at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension T) without any water entering inside is

Water cannot penetrate till the hydrostatic pressure is greater than the excess of pressure that comes into play due to surface tension. at the limiting condition when water just about to penetrates, these two pressure should be equal. 

That is $\mathrm{hdg}=\frac{2\mathrm{T}}{\mathrm{r}}\Rightarrow \mathrm{h}=\frac{2\mathrm{T}}{\mathrm{rdg}}$