Gravitation

We will use Archimedes principle that a floating body displaces its weight.

If the body has volume $V$ and weight $W$ and the densities of the liquid and of water are $\rho_L$ and $\rho_W$ we can write

$\frac{2}{3}V\rho_W=M$

$\frac{1}{4}V\rho_L=M$

$\implies\frac{2}{3}\rho_W=\frac{1}{4}\rho_L$

$\implies\frac{\rho_L}{\rho_W}=\frac{8}{3}$

Taking the density of water to be $1000 kg m^{-3}$ gives the answer

$\rho_L=\frac{8}{3}\times 10^{3}kg m^{-3}$