Question

If a bocy possesses symmetry, ir is possible to take advantageof that symmetry in locating the center of mass.

If the body has a line of symmetry, show that the center of mass lies on that line.

Answer 1

Yes, symmetry gives an indication on where with reference to center of the body the center of mass should be lying.

Like of its a sphere then its in center, if its a cube then at the intersections of the diagonals etc.

Assuming the center of mass doesn't lie on the line of symmetry then there has to be some mass of body unevenly distributed somewhere in either of the parts divided by line of symmetry. But then there will not be a symmetry line. So we can say that whenever there is a symmetry line then center of mass will surely lie on that line.