  We study motion of a point-like impurity in a Bose-Einstein condensate at
T=0. By solving the Gross-Pitaevskii equation in a perturbative manner we
calculate the induced mass of the impurity and the drag force on the impurity
in 3D, 2D and 1D cases. The relationship between the induced mass and the
normal mass of fluid is found and coincides with the result of the Bogoliubov
theory. The drag force appears for supersonic motion of the impurity. In 1D the
drag force is investigated also on the basis of the exact Lieb-Liniger theory,
using the dynamic form factor, which has been evaluated by the Haldane method
of the calculation of correlation functions. In this theory the force appears
for an arbitrarily small velocity of the impurity. The possibility of measuring
the form factor in existing experiments is noted.
