  The celebrated Stokes Law (SL) of hydrodynamics predicts that the velocity of
a particle pulled through a liquid by an external force, Fex, is directly
proportional to the force and inversely proportional to the friction {\zeta}
acted by the medium on the particle. We investigate the range of validity of
Stokes Law at molecular length scales by employing computer simulations to
calculate friction by pulling a tagged particle with a constant force. We thus
calculate friction for two model interaction potentials, Lennard-Jones, and
soft sphere, for several particle sizes, ranging from radius (a) smaller than
the solvent particles to three times larger. We next obtain friction from
diffusion (D) by using Einstein's relation between diffusion and friction
{\zeta} in an unperturbed liquid. We find, to our surprise, a quantitative
agreement between the two at a small-to-intermediate pulling force regime for
all the sizes studied. The Law does break down at a large pulling force beyond
a threshold value. Importantly, the range of validity of Stokes' scheme to
obtain friction increases substantially if we turn off the attractive part of
the interaction potential. Additionally, we calculate the viscosity ({\eta}) of
the unperturbed liquid and find a good agreement with the Stokes-Einstein
relation {\zeta}=C{\eta}a for the viscosity dependence with a value of C close
to 5 {\pi}, that is intermediate between the slip and stick boundary condition.
