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. Read and record with values of M and \(m_1\). Balance the metre rule horizontally on the knife edge. Read and record the balance point as G. Tie a loop of thread around the neck of the measuring cylinder. Fill the cylinder with the sand provided to the 2cm\(^{3}\) mark. Record the volume, V, of the sand. 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. Read and record the new balance position K. Determine the value of e and f. Determine the mass, \(m_2\), of the sand in the measuring cylinder. Hint: \(m_2\) = (\(\frac{\text {M x f}}{e}\)) - \(m_1\). 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. Tabulate your readings. Plot a graph with \(m_2\) on the vertical axis and V on the horizontal axis. Determine the slope, s, of the graph. 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\(^{-3}\)]