## Tuesday, January 5, 2016

### Shift in Centre of Mass when a new mass added

Adding a new mass to the existing system automatically alter the center of mass of the existing system. As extra mass is added to the system, that extra mass also shows its influence on the motion of the system and hence new center of mass will be generated to the system. It actually shifts towards the heavier part of the system.

Center of mass is a point of  a system which represents the actual motion of the system. For any system, it is some where in the system and it can have coordinates along three axes of the Cartesian coordinate system.

Here in this post we would like to solve a small problem in the given video lecture below to demonstrate the impact of adding a new mass to the existing system.

In the given problem, three particles of different masses has center of mass some where. Now as per the given problem, a new mass is added to the system, its center of mass is shifted to orizion of the system. So we can equate each coordinate of center of mass to zero.

By simplifying the given mathematical equation and using the value from the data of the first condition given in the problem, we can find the position of the fourth particle added to the system as shown below.

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