When a razor blade is made to float on water, three forces act on the blade.
(i) Weight of the blade acting vertically downwards.
(ii) Reacting on blade exerted by the liquid surface acting, vertically upwards.
(iii) Force of surface tension on circumference of the blade acting tangentially to the liquid surface.
In this case, as no portion of razor blade is immersed in water, hence Archimede's Principle is not applicable.
