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Center of Mass Calculator
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The Center of mass of a system is the point at which the system's whole mass is concentrated. If there are n no of particles then Center of mass is the position where the average mass of the particle is concentrated.
The Center of Mass Calculator calculates the center of mass of any number of bodies if their respective masses and distances are given.

## Steps for Center of Mass Calculator

Step 1 :

Read the problem and list out the given parameters.

Step 2 :

To find center of mass for any number of bodies of mass m1, m2.... having distances x1,x2....., use the formula:

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

Substitute the given values in the formula and get the Center of mass.

## Problems on Center of Mass Calculator

1. ### Two kids of mass 10 kg and  12 kg are sitting on the two ends of a wooden log, if they are 5m away from each other. Calculate the Center of mass.

Step 1 :

given:

m1 = 10 Kg,

m2 = 12 Kg,

r1 = 0 m,

r2 = 5 m.

Step 2 :

Since there are two bodies

The Center of mass is given by:

xc = $\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

xc = $\frac{10 \times 0 + 12 \times 5}{10 + 12}$
= 2.72 m

The Center of mass is xc = 2.72 m.

2. ### Two bodies of masses 2 kg and 3 kg are kept at a distance of 1m. Calculate its center of mass.

Step 1 :

m1 = 2 Kg,

m2 = 3 Kg,

r1 = 0 m,

r2 = 1 m.

Step 2 :

Since there are two bodies

The Center of mass is given by:

xc = $\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

xc = $\frac{2 \times 0 + 3 \times 1}{2 + 3}$
= 0.6 m

The Center of mass is xc = 0.6 m.

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