Explanation:
Archimedes principle states that the buoyant force on an object ''floating'' in a liquid (say water) is equal to the weight of the liquid displaced.
[tex]F_b=-\rho Vg[/tex]
where p = density of the liquid, g = acceleration due to gravity, and V = volume of the liquid displaced.
Now, how do we determine the density p of the liquid?
We can perform the following experiment.
We can take an object of known weight and drop it in water. The condition is that the object will float. If the object floats, this means that the buoyant force equals the weight of the object. Therefore, we have
[tex]F_b=W[/tex]
which gives us
[tex]W=\rho Vg[/tex]
solving for p gives
[tex]\boxed{\rho=\frac{W}{Vg}\text{.}}[/tex]
Hence, knowing the volume of the liquid displaced and the weight of the floating object, we can determine the density of the liquid.
