A straight rod of length L has one of its end at the origin and the other at `X=L`. If the mass per unit length of the rod is given by `Ax` where A is constant, where is its centre of mass?

Explanation

To find the center of mass of a straight rod of length L with a mass per unit length given by \( Ax \), where \( A \) is a constant, we can follow these steps:

### Step 1: Define the system
We have a straight rod positioned along the x-axis, with one end at the origin (0,0) and the other end at \( x = L \). The mass per unit length of the rod is given by \( \lambda(x) = Ax \).

### Step 2: Express the differential mass element
The differential mass \( dm \) of a small segment of the rod of length \( dx \) at a distance \( x \) from the origin is given by:
\[
...