The distance of centre of mass from end A of a one dimensional rod (AB) having mass density \( \rho = \rho_0 \left(1 - \dfrac{x^2}{L^2}\right) \, \text{kg/m} \) and length \( L \) (in meter) is \( \dfrac{3L}{\alpha} \, \text{m} \). The value of \( \alpha \) is ________. (where \( x \) is the distance from end A)
