2 The region bounded by the \(x\)-axis, the lines \(x = 1\) and \(x = 2\), and the curve \(y = k x ^ { 2 }\), where \(k\) is a positive constant, is occupied by a uniform lamina.
- Find the exact \(x\)-coordinate of the centre of mass of the lamina.
- Given that the \(x\) - and \(y\)-coordinates of the centre of mass of the lamina are equal, find the exact value of \(k\).