Fluid Statics - net upward force

[Roodles01]

Homework Statement

Find magnitude of net upward force on a cube in terms of l, ρ (rho), g and h. then show that h = m/ρl²

A solid cube, mass m, side length l, is placed in a liquid of uniform density, ρ(rho), at a depth h0 below the surface of the liquid, which is open to the air.
The upper and lower faces of the cube are horizontal.

(this is from previous question https://www.physicsforums.com/threads/force-exerted-by-fluid.784711/)

Homework Equations

pressure, p = ρ g h
mass = ρ x volume of liquid displaced

The Attempt at a Solution

Net force, F_n = (p_bottom x area of cube face) - (p_top x area of cube face)
p at top face = (p_T) x ρ_liquid x h x g
p at bottom face = (p_B) x ρ_liquid x (h+l) x g
so
F_n = (ρgh + ρlg - ρgh)
F_n = ρlg

Net force - fine.
Er! how do I show that h = m/ρl²
I know m = ρ x v . . .

 

[haruspex]

Er! how do I show that h = m/ρl²

I can only make sense of the question if h is different from h₀. (Your working all has h, but the question used h₀.)
A reasonable meaning for h would be that the block is released and floats level with depth h immersed.

 

[Roodles01]

I can only make sense of the question if h is different from h₀. (Your working all has h, but the question used h₀.)
A reasonable meaning for h would be that the block is released and floats level with depth h immersed.

I have looked at the question and unscrewed the bits of paper I attempted my answers on and the h0 seems to be a complete typo, it all says just plain h. I will try to work through with that in mind, as you say.