If the origin of co-ordinate system lies at the centre of...

If the origin of co-ordinate system lies at the centre of mass, the sum of the moments of the masses of the system about the centre of mass
(a) may be greater than zero
(b) may be less than zero
(c) may be equal to zero
(d) is always zero

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Key Concepts

Center of Mass

The center of mass of a system is the weighted average of the positions of all the masses in the system. It is the effective point where the total mass of the system can be considered to be concentrated. Setting the origin at the center of mass simplifies many calculations in mechanics because this point has special symmetry properties.

Moment about a Point

The moment of a mass about a point is the product of the mass and its displacement from that point. When summing the moments of all masses in a system, if the point chosen is the center of mass, the sum is zero due to the definition of the center of mass as the balance point where mass-weighted displacements cancel out.

Choice of Coordinate System

Choosing a coordinate system with the origin at the center of mass is a strategic simplification in mechanics. This transformation results in the property that the sum of the accumulated mass moments about the center of mass is zero, which is particularly useful in solving problems related to dynamics and statics.

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