You are provided with a uniform metre rule of mass, M indicated on its reverse side, a knife-edge, a graduated measuring cylinder of known mass, M\(_{1}\) marked on it and other necessary apparatus.

1. Read and record with values of M and m\(_{1}\). 
2. Balance the metre rule horizontally on the knife edge. Read and record the balance point as G.
3. Tie a loop of thread around the neck of the measuring cylinder.
4. Fill the cylinder with the sand provided to the 2cm\(^{3}\) mark. Record the volume, V, of the sand.
5. Hang the cylinder at the 2 cm mark of the metre rule and adjust the position of the knife edge until the rule balances horizontally.
6. Read and record the new balance position K.
7. Determine the value of e and f.
8. Determine the mass, m\(_{2}\), of the sand in the measuring cylinder. Hint: m\(_{2}\) = (\(\frac{\text {M x f}}{e}\)) - m\(_{1}\).
9. Repeat the procedure by filling the measuring cylinder to the mark V = 4,6,8 and 10 cm\(^{3}\). In each case, ensure that the measuring cylinder is kept constant at the 2 cm mark on the metre rule.
10. Tabulate your readings.
11. Plot a graph with m\(_{2}\) on the vertical axis and V on the horizontal axis.
12. Determine the slope, s, of the graph.
13. State two precautions taken to ensure accurate results.

(b)i. Determine the mass of 7.5 cm\(^{3}\) of the sand using your graph.

ii. A gold coin of mass 102.0 g has a uniform cross-sectional area of 10.0 cm\(^{2}\). Calculate its thickness. [Density of gold=19.3 g cm\(^{-3}\)]