Consider these cubes made of different material (densities shown in picture). How high will they float in water (density 1 g/cm³)

Answer

It’s all about weight of the block (W=ρ_oVg) vs the maximum upthrust (U_max=ρ_fVg)

• If ρ_o > ρ_f , then W > U_max.
  • The object will sink all the way down (where NCF comes to the rescue)
• If ρ_o = ρ_f, then W = U_max.
  • The object will neither sink nor float.
  • It can hover at equilibrium at any depth in the fluid as long as it is fully submerged.
• If ρ_o < ρ_f, then W < U_max.
  • The object will float partially submerged.
  • It will displace just enough fluid to generate the amount of upthrust exactly equal to its weight.
  • The lower the object’s density, the higher it will float.
  • In fact, the fraction of volume submerged is equal to the relative density. So cork, wood and ice float with 1/4, 2/3 and 9/10 of their volume below the water surface respectively.

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