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
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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