[10 Marks] 4. A thin metal plate whose lamina is in the shape of a square with sides of length 'a'. The density of the material in the lamina is p(x,

y) = k(x² + y²). (a) Plot the square (ignore thickness of the plate) with vertices at (0,0), (0, a),(a, a),(a,0) as a graph and shade the area of the lamina. (b) Calculate the mass m. (c) Find the moments My and My (d) Find the centre of mass (x, y). r C O D 10 M 6 A In W A = 6 [2 marks] [2 marks] [4 Marks] [2 marks] AR [10 Marks]