LNCT GROUP OF COLLEGES 
        
        
        
        
       Name of Faculty: Dr.Yogesh Dewang 
       Designation: Associate Professor 
       Department: Mechanical Engineering 
       Subject: Engineering Mechanics (BT-204) 
       Unit: 5 
       Topic: Numerical problems on Centroid 
       & Moment of Inertia 
        
        
        
        
        
        
        
       LNCT GROUP OF COLLEGES 
        
            “Numerical problems on Centroid & Moment of Inertia” 
        
       Q.1. Determine the position of the centroid of I-section as shown in Fig. 1. 
        
                                             
                         Figure.1 
       Solution: 1: 
       Refer to Fig. 1 
       Divide the composite figure into there simple areas : 
       (i) Rectangle (10 cm × 2 cm) – top flange ... (1) 
       (ii) Rectangle (25 cm × 2 cm) – web ... (2) 
       (iii) Rectangle (15 cm × 3 cm) – bottom flange ... (3) 
        
        
              LNCT GROUP OF COLLEGES 
               
              To determine the location of the centroid of the plane figure we have the following table: 
                                                 2                                     3
              Components            Area “a” (cm )        Centroidal distance   Ay (cm ) 
                                                          “y” from LL (cm) 
              Rectangle (1)         10×2  = 20            29                    580 
              Rectangle (2)         25 × 2 = 50           15.5                  775 
              Rectangle 3)          15× 3 = 45            1.5                   67.5 
               
                                                                               
               
              Q.2. Using the analytical method, determine the centre of gravity of the plane uniform 
              lamina shown in Fig. 2. 
                                                                                              
                                                     Figure.2 
              Solution: 2: The area of these components, their centroidal distances from the LL-axis and 
              MM-axis and the moments of the areas of individual components about LL-axis and MM-
              axis are tabulated below: 
               
               
               
                LNCT GROUP OF COLLEGES 
                 
                                                                                        2               2
                Components  Area(a)             Centroidal      Centroidal      ax (cm )         ay (cm ) 
                                    2
                                (cm )           distance ‘x’    distance ‘y’ 
                                                From  MM  From             LL 
                                                (cm)            (cm) 
                Triangle (1)    (5×5)/2     =  2.5 + 5 + 2.5  5  +  5/3  =  125                  83.4 
                                12.50           = 10            6.67 
                                          2
                Semi-circle     (Π  ×  2.5 )/2  2.5-            2.5             14.14            24.55 
                (2)             = 9.82          (4×2.5)/3π 
                Rectangle (3)  10×5 = 50.00  2.5 + 5 = 7.5      2.5             375              125 
                                72.32 (Σa)            ---             ---       514.14           232.95 
                Total                                                           (Σax)            (Σay) 
                 
                                                                                              
                 
                Q.3. Determine the location of the centroid of the plane figure shown in Fig. 3. 
                                                                                                    
                                                           Figure.3