It is given that a straight rod has one end at the origin (that is (0,0)) and the other end at the point (L,0) and a linear density given by, where a is a known constant and x is the x coordinate.
Therefore, the infinitesimal mass is given as:
Therefore, the total mass will be the integration of the above equation as:
Therefore,
<u>Now, we can find the center of mass</u>, of the rod as:
Now, we have
x_{cm}=\frac{1}{\frac{aL^3}{3}}\int_{0}^{L}ax^3dx=\frac{3}{aL^3}\times [\frac{ax^4}{4}]_{0}^{L}
Therefore, the center of mass, is at: