7 The region bounded by the curve \(y = x ^ { 3 } - 3 x ^ { 2 } + 4\), the positive \(x\)-axis and the positive \(y\)-axis is occupied by a uniform lamina L . The vertices of L are O , A and B , where O is the origin, A is a point on the positive \(x\)-axis and B is a point on the positive \(y\)-axis (see diagram).
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1. Determine the coordinates of the centre of mass of L . The lamina L is the cross-section through the centre of mass of a uniform solid prism M .
   The prism M is placed on an inclined plane, which makes an angle of \(30 ^ { \circ }\) with the horizontal, so that OA lies along a line of greatest slope of the plane with O lower down the plane than A . It is given that M does not slip on the plane.
2. Determine whether M will topple in this case. Give a reason to support your answer. The prism M is now placed on the same inclined plane so that OB lies along a line of greatest slope of the plane with O lower down the plane than B . It is given that M still does not slip on the plane.
3. Determine whether M will topple in this case. Give a reason to support your answer.