# The x- coordinates of the particles of a system of bodies whose centre of mass is at origin will be?

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The x- coordinates of the particles of a system of bodies whose centre of mass is at origin will be?
1. always positive for all particles
2. always negative for all the particles
3. positive for some particles and negative for other particles
4. none of these

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Correct Answer - Option 3 : positive for some particles and negative for other particles

The correct answer is option 3) i.e. positive for some particles and negative for other particles.

CONCEPT:

• Centre of mass: It is the point of a body where the whole mass of the body is assumed to be concentrated.
• The Centre of mass is also the point about which each particle of a body is symmetrically distributed on all sides.

EXPLANATION:

• If the centre of mass is at the origin, this means that some particles will be towards the left of the COM and some towards the right of the COM.
• The particles towards the left of COM will have a negative value of X-coordinate whereas those towards the right will have a positive value of X-coordinate.
• In this case, the particles can not have always positive values of X-coordinates or always negative values of X-coordinates separately because the particles are uniformly distributed about the centre of mass of the body.