Archimedes' principle is also helpful to determine the density of an object. The ratio in the weights of a body with an equal volume of liquid is the same as in their densities.

             

Let, the Density of the object = D 

Density of the liquid  = $\rho$ 

Weight of the object = $w_{1}$

Weight of equal volume of liquid = w = $w_{1} – w_{2}$

 

Here $w_{2}$ is the weight of the solids in a liquid.  According to Archimedes' principle, $w_{2}$ is less than its actual weight $w_{1}$ by an amount w.

 

Since, $\frac{(D )}{\rho}$=$\frac{(w_{1})}{w}$

D = $\frac{(w_{1}- w_{2})}{w}\times\rho$

 

Or, D = $\frac{(w_{1})}{(w_{1}- w_{2})}\times \rho$     ………………(i)

 

Thus, by finding the weight of the solid in the air $w_{1}$ and its weight in water $w_{2}$, we can calculate the density of the solid by using equation (i) as illustrated in the following example.