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

(N/A) Hershey and Chase worked with bacteriophages and $E. coli$ to prove that $DNA$ is the genetic material. They used different radioactive isotopes to label the $DNA$ and the protein coat of the bacteriophage.
They grew some bacteriophages on a medium containing radioactive phosphorus $(^{32}P)$ to label the $DNA$ and some on a medium containing radioactive sulphur $(^{35}S)$ to label the protein.
Then,these radioactively labelled phages were allowed to infect $E. coli$ bacteria. After infection,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 settled at the bottom of the centrifuge tube.
It was observed that radioactive $(^{32}P)$ was present in the bacterial cells,while radioactive $(^{35}S)$ was found in the supernatant. Hence,it was proved that $DNA$ is the genetic material as it was transferred from the virus to the bacteria.