A sphere of iron and another of wood of the same radius are held under water. Compare the upthrust on the two spheres.

[Hint — Both have equal volume inside water.]

Let density of water be ρ_w

Since radius of both spheres are same hence their volume will be equal.
Let volume of iron sphere = volume of wood sphere = V

Upthrust on Iron sphere = Upthrust_iron = Vρ_wg

Upthrust on Wood sphere = Upthrust_wood = Vρ_wg

∵ Volume of iron sphere and volume of wood sphere is same hence, upthrust by water acting on both the spheres is same.

Comparing the upthrust on the two spheres:

$\dfrac{\text{Upthrust}${\text{iron}}}{\text{Upthrust}{\text{wood}}} = \dfrac{Vρwg}{Vρwg} \\[0.5em] \dfrac{\text{Upthrust}{\text{iron}}}{\text{Upthrust}{\text{wood}}} = \dfrac{1}{1}

∴ Upthrust_iron : Upthrust_wood = 1:1