  For any locally free coherent sheaf on a fixed smooth projective curve, we
study the class, in the Grothendieck ring of varieties, of the Quot scheme that
parametrizes zero-dimensional quotients of the sheaf. We prove that this class
depends only on the rank of the sheaf and on the length of the quotients. As an
application, we obtain an explicit formula that expresses it in terms of the
symmetric products of the curve.
