A solid block with mass $$ is fully immersed in a liquid. It is held at rest by a string above the block. Denote the density of the block by $$ and the density of the liquid by $.($a$)(10$ marks$)$ Obtain an expression for the tension $$ of the string in terms of $,,$ and $.($b$)(5$ marks$)$ Suppose that the block is made of tungsten $(=19\mathrm{.}3$ g$/$cm$)$ and has mass $=20$ kg$.$ If the maximum tension that the string can withstand is $180$ N$,$ and the liquid is water, will the string break? $($c$)(5$ marks$)$ If we now submerge a $10$ kg block of palladium $(=12\mathrm{.}0$ g$/$cm$)$ into mercury $($which is liquid at room temperature, with $=13\mathrm{.}5$ g$/$cm$),$ what is the tension in the string according to your answer to part $($a$)?$ What does this result mean physically?