Question

Select the correct statement from the following: The position of the centre of mass of a system:

• A. Remains the same in any translatory motion
• B. Depend on the choice of coordinates
• C. Does not depend on the shape and size of the system
• D. Depends on the distribution of its mass

Hint:

Centre of mass depends only on how mass is distributed, not on motion or coordinate system choice.

Answer 1

The Correct Option is D

Step 1: Understand centre of mass.
The centre of mass is the point where the entire mass of a system can be considered to be concentrated for motion analysis.

Step 2: Dependence on mass distribution.
The position of centre of mass depends on how mass is distributed in the system. Different distributions give different positions.

Step 3: Analyze option (A).
In translatory motion, the centre of mass moves along with the body, so it does not remain fixed. Hence incorrect.

Step 4: Analyze option (B).
The position changes with coordinate system representation but physical location remains independent. Hence incorrect.

Step 5: Analyze option (C).
Shape and size influence how mass is distributed, so this statement is incorrect.

Step 6: Analyze option (D).
This is correct because centre of mass is determined by mass distribution.

Step 7: Final conclusion.
\[ \boxed{\text{Depends on the distribution of its mass}} \]