Calculate the position of the centroid from MO of the lamina shown in FIGURE 2 below.

Here are the solutions to Question 4.3: QUESTION 4.3 Calculate the position of the centroid from MO of the lamina shown in FIGURE 2 below. To find the position of the centroid from MO (which is the y-axis), we need to calculate the x coordinate of the centroid. We will divide the lamina into three rectangular shapes. Let the origin be at point O. Step 1: Divide the lamina into simple shapes and calculate their areas and centroid x-coordinates. Shape 1 (Leftmost rectangle): Width (w_1) = 200 mm Height (h_1) = 400 mm Area A_1 = w_1 × h_1 = 200 mm × 400 mm = 80000 mm^2 Centroid x-coordinate x_1 = (w_1)/(2) = 200 mm2 = 100 mm Shape 2 (Middle rectangle): Width (w_2) = 250 mm Height (h_2) = 220 mm Area A_2 = w_2 × h_2 = 250 mm × 220 mm = 55000 mm^2 Centroid x-coordinate x_2 = 200 mm + (w_2)/(2) = 200 mm + 250 mm2 = 200 mm + 125 mm = 325 mm Shape 3 (Rightmost rectangle): Width (w_3) = 300 mm Height (h_3) = 90 mm Area A_3 = w_3 × h_3 = 300 mm × 90 mm = 27000 mm^2 Centroid x-coordinate x_3 = 200 mm + 250 mm + (w_3)/(2) = 450 mm + 300 mm2 = 450 mm + 150 mm = 600 mm Step 2: Calculate the total area of the lamina. A_total = A_1 + A_2 + A_3 A_total = 80000 mm^2 + 55000 mm^2 + 27000 mm^2 = 162000 mm^2 Step 3: Calculate the x-coordinate of the centroid (x) using the formula for composite areas. x = (A_1 x_1 + A_2 x_2 + A_3 x_3)/(A_total) x = (80000 mm^2)(100 mm) + (55000 mm^2)(325 mm) + (27000 mm^2)(600 mm)162000 mm^2 x = 8000000 mm^3 + 17875000 mm^3 + 16200000 mm^3162000 mm^2 x = 42075000 mm^3162000 mm^2 x ≈ 259.72 mm The position of the centroid from MO is 259.72 mm. What's next?