Question

Q. 1. Determine the center of gravity and area moment of inertia about centroidal axes of shaded area as shown in Figure 1. [10] 10 cm 10 cm 4 cm 5 cm X 20 cm Figure 1.​

Answer 1

Explanation:

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Answer 2

Given,

              Breadth of triangle (b) = 20cm

              total height of triangle (h) = 25cm

To Find:

• The centre of gravity and area moment of inertia about centroidal axes of shaded area?

Explanation:

as we know that,

                              Area of triangle = $\frac{1}{2}$×$b$×$h$

                                                         = $\frac{1}{2}$×$20$×$25$

                                                         = $250 cm^{2}$

Now,

as length and width has given of the shaded area,

                          length(l) = 10cm

                          breadth(b) = 4cm

                Area of rectangle = $l$ × $b$

                                              = $10$×$4$

                                              = $40 cm^{2}$

      Area of shaded region = Area of triangle - Area of rectangle

                                             = $250 - 40 cm^{2}$

                                             = $210 cm^{2}$

Hence the area moment of inertia about centroidal axes of the shaded region is 210$cm^{2}$