Question $7\mathrm{.}3$

A solid block with mass $m$ 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 ${}_L.$

$($a$)(10$ marks$)$ Obtain an expression for the tension $T$ of the string in terms of $m,g,$ and ${}_L.$

$($b$)(5$ marks$)$ Suppose that the block is made of tungsten