b
Let \(\mathrm{V}\) be the volume of the \(1\) load and \(\rho\) its relative density

So, \(Y=\frac{F L}{A \ell_{a}}=\frac{V \rho g L}{A \ell_{a}}\)         \(...(1)\)

When the load is immersed in the liquid, then

\(Y=\frac{F^{\prime} L}{A \ell_{w}}=\frac{(V \rho g-V \times 1 \times g) L}{A \ell_{w}}\)     \(...(2)\)

(... Now net weight \(=\) weight - upthrust) From eqs. \(( 1)\) and \((2),\) we get

\(\frac{\rho}{\ell_{\mathrm{a}}}=\frac{(\rho-1)}{\ell_{\mathrm{w}}}\) or \(\rho=\frac{\ell_{\mathrm{a}}}{\left(\ell_{\mathrm{a}}-\ell_{\mathrm{w}}\right)}\)