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**Patterns: Location Center of mass**

**Description:**Point where we can assume mass of bodies are concentrated. For system of point masses it is calculated by $r_{cm}=m_{1}+m_{2}................+m_{n}m_{1}r_{1}+m_{2}r_{2}........+m_{n}r_{n} $. In case of uniformly distributed mass, we first check symmetry, if object is symetrical then CM will be on symmetrical line and to calculated other coordinates, we will assume object is made of number of similar types of small mass. Now we take small mass $dm$ at distance r and will use the formula of $r_{cm}=M∫dmr $. This can be integrated for entire mass of the object.

If an object is point of symmetry, centre of mass will be at symmetrical point but When some portion of this object is removed or some additional masses added on it then we use superposition principle by assuming cavity as an independent negative mass density system.

**Question may ask**- Location Center of mass of system of particles, rigid body having uniform and non uniform mass distribution, Rigid body with cavity or extra mass added into it.

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