A theoretical and numerical study has been made of the propagation of a ring rippled laser beam in collisionless plasma with dominant relativistic ponderomotive nonlinearity and its effect on the excitation of electron plasma wave and stimulated Raman backscattering process. The growth of ring ripple, riding on an intense Gaussian laser beam in plasma has also been studied. A paraxial-ray and WKB approximation has been invoked to understand the nature of propagation of the ring rippled Gaussian laser beam in plasma, electron plasma wave and back reflectivity under the influence of both nonlinearities. The growth rate and focusing of a ring rippled beam is found to be considerably affected by the power of the main beam and the phase angle between the electric vectors of the main beam and the ring ripple. It has also been observed that the focusing is released by the coupling of relativistic and ponderomotive nonlinearities, which significantly affected the dynamics of the excitation of electron plasma wave and back reflectivity of stimulated Raman scattering (SRS). Due to the strong coupling between ring rippled laser beam and the excited electron plasma wave, back reflectivity of SRS is enhanced. It has been observed from the computational results that the effect of the increased intensity leads to suppression of SRS back reflectivity. The results have been presented for established laser and plasma parameters.