# Center Of Mass Formula

All the bodies have a point where its total mass is concentrated, and we can lift it by applying force on that particular point.

Center of mass is the unique point where the weighted relative position of the distributed mass sums to zero or the point where if a force is applied causes it to move in the direction of strength.

Center of Mass refers to a point where whole body’s mass is concentrated.

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

$X\,&space;=\,&space;\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}$

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

$X\,&space;=\,&space;\frac{m_{1}x_{1}+m_{2}x_{2}+.......+m_{n}x_{n}}{m_{1}+m_{2}+.......+m_{n}}\,&space;=\,&space;\frac{\Sigma&space;m_{i}x_{i}}{\Sigma&space;m_{i}}$

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

Example 1

Determine the Center of the mass of the two bodies having weights of 2 Kg and 3kg separated by the distance of 10 cm.

Solution

Given parameters are

m1 = 2 Kg,

m2 = 3 Kg,

x1 = 0 m,

x2 = 0.10 m.

The Center of mass formula is expressed as

X = m1x1+m2x2 / m1+m2

= 2×0 + 3×10 / 2 + 3

= 30 / 5

= 6 cm.

Example 2

Calculate the Center of the mass of the system having masses 7 Kg, 4 Kg and 3 Kg along the x-axis having distance 5 cm, 6 cm, and 8 cm?

Solution

Given parameters are

m1 = 7 Kg

m2 = 3 Kg

m3 = 4 Kg

x1 = 5 cm

x2 = 6 cm

x3 = 8 cm

The Center of mass is expressed by X

= m1x1+m2x2+m3x3 / m1+m2+m3

= 7×5+3×6+4×8 / 7+3+4

6.071 cm