26 7. [In this question, you may assume that the centre of mass of a circular arc, radius r, with angle at centre 2α, is a distance sin r α α from the centre.] A B O a a Figure 5 A thin non-uniform metal plate is in the shape of a sector OAB of a circle with centre O and radius a. The angle AOB = 2 π  , as shown in Figure 5. The plate is modelled as a non-uniform lamina. The mass per unit area of the lamina, at any point P of the lamina, is modelled as k (OP)2 , where k = 4 4λ πa and λ is a constant. Using the model, (a) find the mass of the plate in terms of λ , (5) (b) find, in terms of a, the distance of the centre of mass of the plate from O. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________