How did Hershey and Chase differentiate between $DNA$ and protein in their experiment while proving that $DNA$ is the genetic material?

Hershey and Chase worked with bacteriophage and $E .$ coli to prove that $DNA$ is the genetic material. They used different radioactive isotopes to label $DNA$ and protein coat of the bacteriophage.

They grew some bacteriophages on a medium containing radioactive phosphorus $\left(^{32} \mathrm{P}\right)$ to identify $DNA$ and some on a medium containing radioactive sulphur $\left(^{35} \mathrm{S}\right)$ to identify protein. Then, these radioactive labelled phages were allowed to infect $E.$coli bacteria. After infecting, the protein coat of the bacteriophage was separated from the bacterial cell by blending and then subjected to the process of centrifugation. since the protein coat was lighter, it was found in the supernatant while the infected bacteria got settled at the bottom of the centrifuge tube. Hence, it was proved that $DNA$ is the genetic material as it was transferred from virus to bacteria.