If the linear density of a rod of length L varies as `lambda = A+Bx` , find the position of its centre of mass .

Explanation

To find the position of the center of mass of a rod of length \( L \) with a linear density that varies as \( \lambda = A + Bx \), we can follow these steps:

### Step 1: Define the mass element
The linear density \( \lambda \) is given as \( A + Bx \). The mass element \( dm \) of a small segment \( dx \) of the rod can be expressed as:
\[ dm = \lambda \, dx = (A + Bx) \, dx \]

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