the surface tension Y, of liquid depends on the density,P, acceleration of gravity,g, and the height, h. use the method of dimension to derive the actual relationship between these quantities

Answer 1

surface tension is force/length

I am going to call density rho, not P. P is confusing because usually pressure.

F = m a = rho L^3 * L/s^2

= rho L^4/s^2
so
F/L = rho L^3/s^2
but g is L/s^2
so
F/L = rho L^2 g
if our length scale is h then
Y = F/L = constant * rho h^2 g

By the way, it depends on the polarity of the molecules of fluid. Water molecules attract each other.
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