Solved Example Problems for 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.