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What is the significance of defining the center of mass of a system?


The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system. 
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What is the need of centre of mass?

Is it necessary for centre of mass to lie within the body?

Is it necessary that there should be matter at the centre of mass of system?

A body at rest explodes in three fragments. What is the velocity of the centre of mass of exploded part?

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