Waec 2022 Physics Question 2

You are provided with a loaded boiling tube with a centimeter scale fixed inside it, a transparent vessel filled with water, standard masses 2 g, 5 g and 10 g and a slide vernier caliper. Use the diagram above as a guide to perform the experiment. (i) Use the slide vernier caliper to measure and record the external diameter, D, of the boiling tube. (ii) Evaluate A=0.25 \( \pi D^{2} \), where \( \pi=3.14 \). (iii) Place the loaded boiling tube gently in the water in the transparent vessel such that it floats vertically. (iv) Read and record the depth of immersion, y, from the zero mark of the scale fixed inside the boiling tube. (v) Add a mass, m=2 g to the boiling tube. Read and record the new depth of immersion, y, from the zero mark of the scale. (vi) Evaluate h=(-y), \( \log h \) and \( \log m \). (vii) Repeat the experiment for four other values of m=5 g, 7 g, 10 g and 12 g. In each case, record y and evaluate h, \( \log h \) and \( \log m \). (viii) Tabulate the results. (ix) Plot a graph with \( \log m \) on the vertical axis and \( \log h \) on the horizontal axis starting both axes from the origin (0, 0). (x) Determine the slope, s, of the graph. (xi) Determine the intercept, c, on the vertical axis. (xii) Given that \( \log (A P)=c \), calculate P. (xiii) State two precautions taken to ensure accurate results.

(i) State in full the law on which the experiment in 2(a) is based. (ii) A uniform cylindrical rod is 0.63 m long and it has a cross-sectional area of \( 0.1 m^{2} \). Calculate the depth of immersion of the rod if it floats vertically in a liquid of relative density 1.2 [density of rod \( 720 kg m^{-3} \), g=10 m].