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Q1 (a) State Archimedes' principle and explain the physical mechanism involved [3 marks] 0 Figure 21.1 shows a floating sphere. If the density of the sphere is ps and the density of the fluid of density is pi, find the ratio of the densities (PJ pe)in the case where exactly half of the sphere is submerged (5 marks) Figure 21.1: A cuboid completely submerged in water. (ii) Generalise your answer to part (1) for the case where the fraction of the volume above the surface is a [4 marks] (iii) If a ball weighs 20 g. has a diameter of 4cm and is floating in water with a density of pi= 1000 kgm determine the fraction of the volume which is above the surface. If you do not have an expression for part (ii) then you may use the following incorrect) expression: podpr= (1-2) [5 marks] (b) Figure Q1.2 shows the side wall of a fish tank which is 0.5 m deep and 1 m wide. As a decorative feature, there is a viewing window which is 20cm deep and 80 cm wide which is 10 cm from the bottom, as shown. Calculate the force on the window due to the water if the water is 40 cm deep. [8 marks)

1 m 20 cm || || 50 cm 40 cm 80 cm Figure Q1.2 Wall of a fish tank