Answer to Question #109849 in Molecular Physics | Thermodynamics for Jess

Question

A ball is floating at rest in a fluid.

The ratio of the volume of the fluid displaced, VD, to the volume of the ball, Vball, is:

VD/Vball = 0.79

If the ball has a density of 950 kg m−3 then what is the density of the fluid? (to 2 s.f and in kg m−3)

Answer 1

The ball is floating at rest in a fluid if

$$mg=F_{\rm buoyant}.$$

Hence,

$$g\rho_{\rm ball} V_{\rm ball}=g\rho_{\rm fluid} V_{\rm D}.$$

The density of the fluid

$$\rho_{\rm fluid}= \rho_{\rm ball} V_{\rm ball}/V_{\rm D}=950/0.79=1200\:\rm kg/m^3.$$