8) A plane lamina with uniform density occupies the shaded region in Figure 1. It consists...

Transcribed Image Text:

8) A plane lamina with uniform density occupies the shaded region in Figure 1. It consists of a rectangle (with sides of length a=4 and b = 6) rotated by 45 degrees and has a circular hole (with diameter d = 2.3) at the centre of the rectangle. Two corners of the rectangle touch the x- and y-axes as shown. (a) Determine the x- and y-components of the centroid of the plane lamina. [9 Marks] (b) How would the centroid's location change if we kept everything the same but reduced the diameter of the circle by 50%? b d C [8 Marks] 8) A plane lamina with uniform density occupies the shaded region in Figure 1. It consists of a rectangle (with sides of length a=4 and b = 6) rotated by 45 degrees and has a circular hole (with diameter d = 2.3) at the centre of the rectangle. Two corners of the rectangle touch the x- and y-axes as shown. (a) Determine the x- and y-components of the centroid of the plane lamina. [9 Marks] (b) How would the centroid's location change if we kept everything the same but reduced the diameter of the circle by 50%? b d C [8 Marks]