 Do this question. This is 1 kg, 2 kg, 3 kg, 4 kg, 5 kg, and they are placed on the sides of an imaginary square. The sides of the square is 1 unit. You need to find out the center of mass of this entire system. The system has 5 particles. First thing what you should do, first thing is place your x, y coordinate then only you will have y coordinate of the particles. Your x and y coordinate, what coordinate x is you take should be center of mass somewhere between 4 and 5 because most amount of mass is around that. So, let me take this x axis. What is the coordinate 1 comma 0? This is and this 0.5 comma 0.5 simple. So, x center of mass how do you find that? 1 into 0 plus 2 into 1 plus 3 into 1 plus 4 into 0 plus 5 into 0.5 divided by 15 sum of all the masses and similarly y c n. Y c will be what? 1 into 1, 2 into 1 plus 3 into 0, 4 into 0, 5 into 0.5 divided by 15. Is it simple calculation? Yes or no? What is your coordinate related to this coordinate? But if you take coordinate axis which passes through this point, originally this point center of mass becomes 0 comma 0. So, coordinate depends on what system of particles like this. Need not be there are particles placed at different locations. We have not location. The assumption is particles point masses. Are you getting it? What if the 5 kg mass is a big circle like this which is not located exactly at 0.5 comma 0.5 it is spread across. You cannot say mass of 5 into 0.5 because 0.5 is not a while applying this formula. Let us talk about that. Now suppose your system has 1 is point mass of mass m 2 and this is a bigger mass of mass m 1. Then I will say that this m 1 masses I will divide this m 1 into different point masses starting from small m 1 to small m n. Because the formula I have is for the point mass. I cannot have small small point masses. So, if that is the case then x will be equal to the small point mass inside m 1 into location of this small m 1. That is it. Location of that is x 1. If I divide it into small point masses then I take 1 x 1 plus m 2 x 2 and so on up to m n x n. This will give me summation of entire capital M 1. Then summation of all this will be equal to capital M 1. This plus the second masses of point mass m 2 let us say capital mass m 2. Now see what I am doing. I am multiplying divided by m 1 in the numerator. So, m 1 x 1 m 2 x 2 and so on divided by m 1 plus m 2 plus m 2 x 2 divided by m 1 plus m 2. Now tell me what is the first step in the numerator m 1 into center mass of m 1's location plus m 2 into x 2 divided by m 1 plus m 2. This will be total center of mass. So, if there is a bigger mass you multiply it is center of mass plus m 2 into its center of the system. If mass is uniformly distributed then the center of mass location of center of mass is location of another center. How you can see that x is equal to m 1 x 1 and so on. If mass is uniformly distributed all the points and this is a uniformly distributed to the distribution of mass then the center of mass will lie center of mass because it should lie of both the mass. For example center of mass which is not regular shape and size. This one because there will be infinite particles and also there will not be any line of symmetry to help me out. Then how to find center of mass will get transformed into integral type and this is how it will happen. So, x center of mass is summation of m i. Now I am saying that suppose there is a big mass. I will assume that the entire big object is made up of small small masses of mass dm. dm is the small mass and its location is x. The location of dm is x. So, the numerator will become what integral of x dm divided by summation we get transformed into integral integration is now can you integrate that I cannot integrate this. So, first of all second there are two variables x and dm. Similarly here this is a formula which you have to solve for different different objects. Any doubts? No.