Find the centre of mass of a triangular lamina.
(N/A) The triangular lamina $(\Delta LMN)$ can be subdivided into narrow strips,each parallel to the base $(MN)$.
By symmetry,each strip has its centre of mass at its midpoint.
If we join the midpoints of all such strips,we obtain the median $LP$.
Therefore,the centre of mass of the entire triangle must lie on the median $LP$.
Similarly,by considering strips parallel to other sides,we can argue that the centre of mass must also lie on the medians $MQ$ and $NR$.
Since the centre of mass lies on all three medians,it must be located at their point of concurrence,which is the centroid $G$ of the triangle.
By symmetry,each strip has its centre of mass at its midpoint.
If we join the midpoints of all such strips,we obtain the median $LP$.
Therefore,the centre of mass of the entire triangle must lie on the median $LP$.
Similarly,by considering strips parallel to other sides,we can argue that the centre of mass must also lie on the medians $MQ$ and $NR$.
Since the centre of mass lies on all three medians,it must be located at their point of concurrence,which is the centroid $G$ of the triangle.
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