Question

The centre of mass always lies on the axis of symmetry if it exists. Is this statement true or false?​

Answer 1

I think the answer is true

Answer 2

The statement is false.

• The centre of mass of a symmetrical body will lie on its axis of symmetry.
• For example: The centre of mass of a solid cube will pass from its centre or body diagonal as these are the axes of symmetry for the cube.
• But the second condition is that the the body must have uniform mass distribution otherwise this statement will not hold true.
• Therefore the statement given in the question is not true since it does not mentions both the conditions of COM.