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# Center of Mass Calculator

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Online center of mass calculator helps to find out the center of mass of a system of masses. It means that in a single point all masses are concentrated. The formula to find out the center of mass of a system is,
$X_{cm}$ = $\frac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}+......+m_{n}x_{n}}{m_{1}+m_{2}+m_{3}+.........+m_{n}}$where,
$m_{1}$, $m_{2}$,$m_{3}$....are masses,
$x_{1}$, $x_{2}$, $x_{3}$......are distance of the masses.

## Steps

Step 1 : Pick out the values given in the question.

Step 2 : Plug these values in the formula which is given above and find out the center of mass.

## Problems

Let us discuss the problems related to center of mass.

### Solved Examples

Question 1: The masses of three substances are given as 10kg, 12kg, 14kg and these are kept at a distance of 0.2m, 0.5m, 0.8m. Calculate the center of mass.

Solution:

Given that,
$m_{1}$ = 10kg, $m_{2}$ = 12kg, $m_{3}$ = 14kg
$x_{1}$ = 0.2m, $x_{2}$ = 0.5m, $x_{3}$ = 0.8m

Center of mass is,

$X_{cm}$ = $\frac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}+......+m_{n}x_{n}}{m_{1}+m_{2}+m_{3}.........+m_{n}}$

So, $X_{cm}$ = $\frac{10\times0.2+12\times0.5+14\times0.8}{10+12+14}$

$X_{cm}$ = $\frac{19.2}{36}$ = 0.533m

Question 2: Find out the center of mass if $m_{1}$ = 5kg, $m_{2}$ = 9kg and $x_{1}$ = 0.45m and $x_{2}$ = 0.30m respectively.

Solution:

Given that,
$m_{1}$ = 5kg, $m_{2}$ = 9kg
$x_{1}$ = 0.45m, $x_{2}$ = 0.30m

Center of mass is,

$X_{cm}$ = $\frac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}+......+m_{n}x_{n}}{m_{1}+m_{2}+m_{3}.........+m_{n}}$

So, $X_{cm}$ = $\frac{5\times0.45+9\times0.30}{5+9}$

$X_{cm}$ = $\frac{4.95}{14}$ = 0.3535m