  The modified quark-meson coupling model, which features a density dependent
bag constant and bag radius in nuclear matter, is checked against the EMC
effect within the framework of dynamical rescaling. Our emphasis is on the
change in the average bag radius in nuclei, as evaluated in a local density
approximation, and its implication for the rescaling parameter. We find that
when the bag constant in nuclear matter is significantly reduced from its
free-space value, the resulting rescaling parameter is in good agreement with
that required to explain the observed depletion of the structure functions in
the medium Bjorken $x$ region. Such a large reduction of the bag constant also
implies large and canceling Lorentz scalar and vector potentials for the
nucleon in nuclear matter which are comparable to those suggested by the
relativistic nuclear phenomenology and finite-density QCD sum rules.
