  We consider a class of $L^2$-supercritical inhomogeneous nonlinear
Schr\"odinger equations in two dimensions
  \[
  i\partial_t u + \Delta u = \pm |x|^{-b} |u|^\alpha u, \quad (t,x) \in
\mathbb{R} \times \mathbb{R}^2,
  \]
  where $0<b<1$ and $\alpha>2-b$. By adapting a new approach of
Arora-Dodson-Murphy \cite{ADM}, we show the energy scattering for the equation
with radially symmetric initial data. In the focusing case, our result extends
the one of Farah-Guzm\'an \cite{FG-high} to the whole range of $b$ where the
local well-posedness is available. In the defocusing case, our result extends
the one in \cite{Dinh-scat} where the energy scattering for non-radial initial
data was established in dimensions $N\geq 3$.
