[UPSC CSE 2018] Conservation Laws (Q16, 15M)

A rod of length L has non-uniform linear mass density (mass per unit length) \lambda, which varies as \lambda=\lambda_0\left(\dfrac{S}{L}\right); where \lambda_0 is a constant and S is the distance from the end marked `O' (as shown in the figure). Find the centre of mass of the rod.