No, the value of g is different at different places on the surface of earth. The shape of the earth is not exactly spherical, it is flattened at the poles and is bulging out at the equator. Due to which the radius of the earth is smaller at poles and is larger at equator. Since \(g\propto\frac{1}{R^2}\) , therefore the acceleration due to gravity is smaller at equator than that at poles.
