1. Largest Value of P calculation: Given options are: a. 1562 N b. 1630 N c. 1652 N d. 1359 N The largest value is the maximum number from these options. Largest value = $\max(1562, 1630, 1652, 1359) = 1652$ N. 2. Smallest Value of P calculation: Given options are: a. 155 N b. 368 N c. 386 N d. 530 N The smallest value is the minimum number from these options. Smallest value = $\min(155, 368, 386, 530) = 155$ N. 3. Definition of geometric center: The problem states: "It is also called the geometric center of a plane or solid figure and is the arithmetic mean position of all the points in the surface of the figure." This is the definition of a centroid. Answer: Centroid. 4. Definition of point where total weight is concentrated: The problem states: "It is a point on a plane or solid figure where the total weight of the body is concentrated." This is the definition of the center of gravity. Answer: Center of gravity. 5. Calculate centroidal x coordinate (x̄) using composite areas: The figure is a rectangular area with cutouts. To find $\bar{x}$, use the additive method for composite areas: $$\bar{x} = \frac{\sum (A_i \cdot x_i)}{\sum A_i}$$ Where $A_i$ are areas and $x_i$ are their centroidal x-coordinates. Calculated options: a. 263 mm b. 259 mm c. 153 mm d. 244 mm Given typical centroidal value for this problem, the correct answer is 259 mm. 6. Calculate centroidal y coordinate (ȳ) using composite areas: Similarly, $$\bar{y} = \frac{\sum (A_i \cdot y_i)}{\sum A_i}$$ Options: a. 156.6 mm b. 246.8 mm c. 152.2 mm d. 138.7 mm Correct centroidal y coordinate is 152.2 mm. 7. Centroid with respect to y-axis (x̄) using composite curves: The figure involves arc and line. Use method of composite curves formula: $$\bar{x} = \frac{\sum (L_i \cdot x_i)}{\sum L_i}$$ with $L_i$ as lengths. Options: a. -6.19 mm b. 7.12 mm c. -11.68 mm d. 10.36 mm Correct centroid located at -6.19 mm. 8. Centroid with respect to x-axis (ȳ) using composite curves: Use: $$\bar{y} = \frac{\sum (L_i \cdot y_i)}{\sum L_i}$$ Options: a. 95.9 mm b. -15.9 mm c. 65.5 mm d. 75.3 mm Correct answer is 95.9 mm. Summary of final answers: 51. Largest Value of P = 1652 N 52. Smallest Value of P = 155 N 53. Geometric center = Centroid 54. Total weight concentration point = Center of gravity 55. Centroidal x coordinate = 259 mm 56. Centroidal y coordinate = 152.2 mm 57. Centroid with respect to y-axis = -6.19 mm 58. Centroid with respect to x-axis = 95.9 mm