OP If you are still here...
Let your son read the Archimedes and the king story and watch Why Ships Float.
Then you and he need to stop with the "I can't do this cos I is a thicko" schtick. Your son has been given an opportunity for independent learning that so few kids get these days. Believe me, it is one of the reasons so many teachers get frustrated. I taught A levels for decades and in my last 5 years it became more and more prevalent for even the very brightest to throw a hissy fit and demand "Just tell us the answer" when tasked with research.
Instead of railing against it embrace it. Sit with him and Google the homework and start by ranking the results:
Too complicated --> too easy
Reliable information --> crackpot flat earthers
Then how to take notes, easy bullet points, no more than 10 initially that he can then reduce, incrementally as he understand more, down to 3-5.
So, he reads the Archimedes and the king story and makes 10 ish notes on the way the gold affects the water.
Then watches How Ships Float and reduces his bullet points as, hopefully, his understanding has increased.
Take those bullet points in as his completed homework, along with references tro the story and youtube clip.
What he has found is that there is a lot of information on Google and that you have to be careful to select the right sites.
What he has also found is that Archimedes was born a very long time ago, that's where we get the word Eureka from. If he read further he would learn not to tell a Roman soldier with a spear to wait a moment...
And he would have a basic working idea of what Archimedes principle is.
Research skills, some history and some science - all in one piece of homework! Rejoice in it. Instil a love of independent learning. Your son will thank you for it one day... many of his teachers far sooner!