10   Question 3 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 11   Question 3 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 3 is 9 marks) 12   4. 18a 12a 18a 6a A M B E D C Figure 1 A uniform triangular lamina ABC is isosceles, with AC = BC. The midpoint of AB is M. The length of AB is 18a and the length of CM is 18a. The triangular lamina CDE, with DE = 6a and CD = 12a, has ED parallel to AB and MDC is a straight line. Triangle CDE is removed from triangle ABC to form the lamina L, shown shaded in Figure 1. The distance of the centre of mass of L from MC is d. (a) Show that d a = 4 7 (4) The lamina L is suspended by two light inextensible strings. One string is attached to L at A and the other string is attached to L at B. The lamina hangs in equilibrium in a vertical plane with the strings vertical and AB horizontal. The weight of L is W (b) Find, in terms of W, the tension in the string attached to L at B (3) The string attached to L at B breaks, so that L is now suspended from A. When L is hanging in equilibrium in a vertical plane, the angle between AB and the downward vertical through A is θ° (c) Find the value of θ (7) Turn over 13   Question 4 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________