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# Center of Mass Formula

Every body has a point where its whole mass is concentrated so we can lift any body, by applying force on that point only.

Center of Mass (COM) is a point where whole body's mass is assumed to be concentrated.

If there are two masses m1 and m2 separated by distances x1 and x2 from a fixed point. The Center of mass (X) is given by

If there are masses m1, m2,.....mn having distances x1, x2,......xn then the Center of mass (X) is given by

Center of Mass Formula is used to find the center of mass of any given number of bodies if their respective masses and distances are known. Since we are finding at what distance Center of mass is located it is expressed in meters (m).

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## Center of Mass Problems

Problems based on center of mass which will be helpful for you.

### Solved Examples

Question 1: Find the Center of mass of the two bodies which are of masses 2 Kg and 3kg separated by the distance of 5 cm?
Solution:

Given: Mass m1 = 2 Kg,
Mass m2 = 3 Kg,
Distance x1 = 0 m,
Distance x2 = 0.05 m.
The Center of mass formula is given by X = $\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$
= $\frac{2 \times 0 + 3 \times 5}{2 + 3}$
= $\frac{15}{5}$
= 3 cm.

Question 2: Find the Center of mass of the system of masses 7 Kg, 4 Kg and 3 Kg along the x-axis having distance 5 cm, 6 cm and 8 cm?
Solution:

Given: Masses m1 = 7 Kg, m2 = 4 Kg, m3 = 3 Kg
Distances x1 = 5 cm, x2 = 6 cm, x3 = 8 cm
The Center of mass is given by X = $\frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$
= $\frac{7 \times 5 + 4 \times 6 + 3 \times 8}{5 + 6 + 8}$
= 4.368 cm
= 0.044 m.

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