  The aim of this paper is to prove two new uncertainty principles for the
Fourier-Bessel transform (or Hankel transform). The first of these results is
an extension of a result of Amrein-Berthier-Benedicks, it states that a non
zero function $f$ and its Fourier-Bessel transform $\mathcal{F}_\alpha (f)$
cannot both have support of finite measure. The second result states that the
supports of $f$ and $\mathcal{F}_\alpha (f)$ cannot both be
$(\eps,\alpha)$-thin, this extending a result of Shubin-Vakilian-Wolff. As a
side result we prove that the dilation of a $\cc_0$-function are linearly
independent. We also extend Faris's local uncertainty principle to the
Fourier-Bessel transform.
