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# An amateur sculptor decides to portray a bird (Fig).Luckily, the final model is actually able to stand upright. The model is formed of a single thick sheet of metal of uniform thickness. Of the points shown, which is most likely to be the center of mass?

Deepak Patra
6 years ago
The center of mass highlights the mass distribution of the system, which depends on the mass of individual particle making it, and its separation from the origin in the corresponding reference frame.
Assume that the origin in this case lies at point 4, and one checks the mass distribution of the sculpture about that point. Divide the sculpture into three blocks: one consisting of the head (Area A), the other consisting of the tail (Area B) and the rest as a body (Area C), as shown in figure below,

It is important to note that the center of mass of the first block lays near point 6, of second block near point 1, and of third block near point 2. The center of mass of the system can now be reduced to about three points, which are 6, 2 and 1 respectively, each containing the total mass of their corresponding blocks.
It can be seen from the figure that the mass of the third block is much larger than that of first and second. Therefore, the center of mass of the sculpture can be expected to be closest to the origin itself, that is, point 4.