
Aim: to measure the Relative
Density of some common solids 
The relative density of a substance is the ratio of
the density of the substance to the density of pure
water. 
Therefore, the R.D. of a substance can be calculated
by comparing the mass (or weight) of a given volume of
the substance with the mass (or weight) of the same
volume of pure water. 

This writer feels that it is a good idea to remind
ourselves that experiments can sometimes be performed
with simple apparatus such as levers and bits of
string... 

The method suggested here is based on the
observations made by Archimedes nearly 2000 years ago. 
For the purposes of this
experiment, the principle of Archimedes can be stated as
follows: 
When a body is under water, it experiences an
apparent loss of weight equal to the weight
of the water it displaces. 

We first measure the real weight, W of a
piece of the solid. 
We then measure the apparent weight, W_{A}
of the same piece of solid when it is completely
immersed in pure water. 
From the preceding, it should be clear that the
relative density can be calculated from the following
equation 

Method 
Use a simple balance, as shown below. 
Obtain an equilibrium first
with the piece of solid in air. 

This allows us to find the position of the mass, m,
corresponding to the real weight, W of
the object. 

Next obtain an equilibrium with the same piece of
solid immersed in water. 

This allows us to find the position of the mass, m,
corresponding to the apparent weight, W_{A}
of the object. 

If we keep m and x constant for each pair
of measurements, we can say that 

and 


therefore we can write 

from which relative density can be easily calculated. 

For each value of relative density measured, work
out the indeterminacy in the result, assuming that the
distances d_{1} and d_{2} are measured
using a ruler marked in mm. 
Then express your answers in the usual form: R.D. =
x ±δx where δx is the indeterminacy. 