A glass flask weighing 390   g , having internal volume 500 cc just floats when half of it is filled…

If $V$is the volume of water displaced, then mass of water displaced is, $m={\rho }_{w}V$

Now, the mass of water displaced is equal to sum of mass of water in flask and mass of flask, therefore,

$$\begin{gathered} \Rightarrow {\rho }_{w}V=m_{flask}+{\rho }_w\left(\frac{500}{2}\right) \\ \Rightarrow 1\times V=390+1\times 250 \\ \Rightarrow V=640 {\mathrm{cm}}^3 \end{gathered}$$

Therefore, the volume of material of flask is, $=V_{\mathrm{outer}}-V_{\mathrm{inner}}=640-500=140 {\mathrm{cm}}^3$

Density of flask's material, ${\rho }_{flask}=\frac{m}{V}=\frac{390}{140}=0.28 \mathrm{g} {\mathrm{cm}}^{-3}$

Specific gravity of the glass flask is, $=\frac{{\rho }_{flask}}{{\rho }_{water}}=2.8$