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

Physics : Motion of System of Particles and Rigid Bodies : Center of mass for uniform distribution of mass

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 : Solved Example Problems for Center of mass for uniform distribution of mass |