Question

Which of the following statement is true regarding the centre of mass of a system?

• A. The centre of mass depends on the size and shape but does not depend on the distribution of mass of the body.
• B. The centre of mass depends on the coordinate system.
• C. The centre of mass of a system depends on the size and shape of the body but independent of the co-ordinate system.
• D. The centre of mass of a body always lies inside the body.

Hint:

The centre of mass is determined by the distribution of mass in the system and is independent of the coordinate system. It does not always lie inside the body.

Answer 1

The Correct Option is C

The centre of mass (CM) of a system is the weighted average position of all the masses in the system. It depends on the mass distribution, shape, and size of the system. However, it is independent of the coordinate system. 
That is, the position of the centre of mass will remain the same regardless of which coordinate system you use. The centre of mass is not influenced by the choice of origin, and it does not necessarily lie within the body; it can lie outside the body in certain cases (e.g., a ring). 
Thus, option (C) is the correct answer.