The template shown in Figure 3 is formed by joining together three separate laminas. All three laminas lie in the same plane. - $$\(P Q U V\)$$ is a uniform square lamina with sides of length $$\(3 a\)$$ - URST is a uniform square lamina with sides of length $$\(6 a\)$$ - $$\(Q R U\)$$ is a uniform triangular lamina with $$\(U Q=3 a, U R=6 a\)$$ and angle $$\(Q U R=90^{\circ}\)$$ The mass per unit area of $$\(P Q U V\)$$ is $$\(k\)$$, where $$\(k\)$$ is a constant. The mass per unit area of URST is $$\(k\)$$. The mass per unit area of $$\(Q R U\)$$ is $$\(2 k\)$$. The distance of the centre of mass of the template from $$\(Q T\)$$ is $$\(d\)$$. (a) Show that $$\(d=\frac{29}{14} a\)$$ (5) The template is freely suspended from the point $$\(Q\)$$ and hangs in equilibrium with $$\(Q R\)$$ at $$\(\theta^{\circ}\)$$ to the downward vertical. (b) Find the value of $$\(\theta\)$$ (7)

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