Consider these cubes made of different material (densities shown in picture). How high will they float in water (density 1 g/cm^{3})

Answer

It’s all about weight of the block (*W*=* ρ_{o}Vg*) vs the maximum upthrust (

*U*=

_{max}*)*

*ρ*Vg_{f}- If
*ρ*>_{o }*ρ*, then_{f }*W*>*U*._{max}- The object will
**sink all the way down**(where*NCF*comes to the rescue)

- The object will
- If
*ρ*=_{o }*ρ*, then_{f}*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*, then_{f}*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.