  We prove that there are rational homology balls $B_p$ smoothly embedded in
the $2$-handlebodies associated to certain knots. Furthermore we show that, if
we rationally blow up the $2$-handlebody along the embedded rational homology
ball $B_p$, then the resulting $4$-manifold cannot be obtained just by a
sequence of ordinary blow ups from the $2$-handlebody under a certain mild
condition.
