Posted On : 27.06.2018 04:00 pm

## Chapter: __11th Physics : UNIT 5 : Motion of System of Particles and Rigid Bodies__

**Center of mass for uniform distribution of mass**

Center of mass for uniform distribution of mass

Center of mass for uniform distribution of mass

If the mass is uniformly distributed in a bulk object, then a small mass (∆m) of the body can be treated as a point mass and the summations can be done to obtain the expressions for the coordinates of center of mass.

On the other hand, if the small mass taken is infinitesimally* small (dm) then, the summations can be replaced by integrations as given below.

## Solved Example Problems for Center of mass for uniform distribution of mass

### Example 5.4

Locate the center of mass of a uniform rod of mass M and length *l*.

*Solution*

Consider a uniform rod of mass M and length whose one end coincides with the origin as shown in Figure. The rod is kept along the x axis. To find the center of mass

of this rod, we choose an infinitesimally small mass dm of elemental length dx at a distance x from the origin.

Now, we can write the center of mass equation for this mass distribution as,

As the position *l*/2 is the geometric center of the rod, it is concluded that the center of mass of the uniform rod is located at its geometric center itself.

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11th Physics : UNIT 5 : Motion of System of Particles and Rigid Bodies : Center of mass for uniform distribution of mass |