The uniform lamina $$\(P Q R S T U V\)$$ shown in Figure 2 is formed from two identical rectangles, $$\(P Q U V\)$$ and $$\(Q R S T U\)$$. The rectangles have sides $$\(P Q=R S=2 a\)$$ and $$\(P V=Q R=k a\)$$. (a) Show that the centre of mass of the lamina is $$\(\left(\frac{6+k}{4}\right) a\)$$ from $$\(P V\)$$ (3) The lamina is freely suspended from $$\(P\)$$ and hangs in equilibrium with $$\(P R\)$$ at an angle of $$\(\alpha\)$$ to the downward vertical. Given that $$\(\tan \alpha=\frac{7}{15}\)$$ (b) find the value of $$\(k\)$$. (6)

Answer:

Knowledge points:

Solution: