2. 
The method suggested
here is based on the observations made by Archimedes nearly 2000
years ago (we like to be uptodate in physics!). 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. 


It can easily
be shown that this principle leads to a very simple way of measuring
the relative density of a solid which is more dense than water. To do
this, we first measure the "real" weight, W of a piece of
the solid and then measure the apparent weight, W_{A} of the
same piece of solid when it is completely immersed in pure water. The
relative density, R. D. can be calculated from the following equation 


3. 
Use a simple
balance, as shown in figure 1. Obtain an equilibrium first with
the piece of solid in air then with the same piece of solid
immersed in water. This allows us to find the position of the
mass, m, corresponding to the real weight of the object. 

figure 1 

Now find the position of
the mass, m, corresponding to the apparent weight of the object
when it is completely immersed in water. 

....
figure 2

4. 
It is
recommended that, for each measurement of R.D., both m and x
remain constant. By combining the definition of R.D. with
the principle of moments you should be able to find an
expression for calculating the R. D. of the solid which includes
only the distances d_{1} and d_{2}. 
5. 
Your
report should include a diagram similar to figure 2 but with
arrows representing the forces relevant your analysis. 
6. 
For each value of relative density measured, work out
the indeterminacy in the result. Then express your answers in the usual
form: R.D. = x ±
x
where
x
is the indeterminacy.
Also calculate the % indeterminacy for each result. 