This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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QUESTION 5.2: CENTRE OF GRAVITY Given: Cylinder diameter D = 50 mm, so radius r = 25 mm Cylinder height h_c = 250 mm Hemisphere diameter D = 50 mm, so radius r = 25 mm Step 1: Calculate the volume and centroid of the cylinder from its base (the table). The volume of the cylinder is V_c = r^2 h_c. V_c = (25 mm)^2 (250 mm) = 156250 mm^3 The centroid of the cylinder from its base is y_c = (h_c)/(2). y_c = 250 mm2 = 125 mm Step 2: Calculate the volume and centroid of the hemisphere from the base of the cylinder (the table). The volume of the hemisphere is V_h = (2)/(3) r^3. V_h = (2)/(3) (25 mm)^3 = (2)/(3) (15625) mm^3 = (31250)/(3) mm^3 The centroid of a hemisphere from its flat base is (3)/(8)r. Since the hemisphere is placed on top of the cylinder, its flat base is at h_c = 250 mm from the table. So, the centroid of the hemisphere from the table is y_h = h_c + (3)/(8)r. y_h = 250 mm + (3)/(8)(25 mm) = 250 mm + 9.375 mm = 259.375 mm Step 3: Calculate the overall centre of gravity Y of the composite body from the table using the formula Y = (V_c y_c + V_h y_h)/(V_c + V_h). Y = (156250 mm^3)(125 mm) + ((31250)/(3) mm^3)(259.375 mm)156250 mm^3 + (31250)/(3) mm^3 We can cancel from all terms: Y = ((156250)(125) + (31250)/(3))(259.375)156250 + (31250)/(3) Y = (19531250 + 2701822.9166...)/(156250 + 10416.6666...) Y = (22233072.9166...)/(166666.6666...) Y ≈ 133.40 mm The centre of gravity of the body from the table is 133.40 mm. What's next?