Question

Find the centre of mass of a triangular lamina.

Answer 1

Answer:

The lamina (ΔLMN) may be subdivided into narrow strips each parallel to the base(MN) as shown in Fig.,

By symmetry each strip has its centre of mass at its midpoint. If we join the midpoint of all the strips we get the median LP. The centre of mass of the triangle as a whole therefore, has to lie on the median LP. Similarly, we can argue that it lies on the median MQ and NR. This means the centre of mass lies on the point of concurrence of the medians, i.e. on the centroid G of the triangle.

Answer 2

Answer:

Then it could be shown that the center of mass is at the intersection of the medians. And by a medium we mean a line that goes from one vertex of the triangle to the midpoint of the opposite.