Physics problem about floating ball

Question

A closed sphere/ball is floating (half of it is in the fluid). The sphere's mass is m, density ρ. What is the formula for finding the volume of the sphere?

The correct answer is 2m/ρ.

Can you show how you get this answer because I got m/ρ (applying Archimedes' principle F=ρgV and making it equal ρgV=mg, thus V=m/ρ

Answer 1

You are on the right track here, and with a small revision can get to the correct answer. Buoyant force does, as you write, equal the weight of the fluid displaced, so ρgV is the correct expression. Note, however, that the volume in this expression refers specifically to that of the displaced water, which equals one-half of the volume of the sphere, as the sphere floats with half its volume above the surface.

If we use the symbol "V" to represent the volume of the sphere, then equating the weight of the sphere to the buoyant force gives the following:



ρg(V/2) = mg

ρ(V/2) = m

V = 2m/ρ