7 In this question you must show detailed reasoning.
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\caption{Fig. 7}
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Fig. 7 shows the curve with equation \(y = \frac { 2 } { 3 } \ln x\). The region R , shown shaded in Fig. 7, is bounded by the curve and the lines \(x = 0 , y = 0\) and \(y = \ln 2\). A uniform solid of revolution is formed by rotating the region R completely about the \(y\)-axis.
Find the exact \(y\)-coordinate of the centre of mass of the solid.