Hydrogen adsorption on graphene sheets is a promising new area of research. The physical interactions between adsorbed molecules and the graphene surface could drastically influence the morphology of the graphene sheet, producing a rippled structure even at very low temperatures when the contribution of thermal agitations is quite negligible. We have employed a series of very accurate molecular dynamics(MD) simulations to reveal the effect of H2 molecules adsorption on graphene nano ribbons (GNRs). To this end,the dependence of the degree of ripple-type distortion of the surface on the H2 coverage is examined. Furthermore, we have also considered the connection between the critical value of the H2 adsorption and the maximum induced deformation on the graphene structure. Overall, our findings provide crucial information for the performance of hydrogenated graphene, especially at very low temperatures.