A cube of external dimension $10\ cm$ has an inner cubical portion of side $5\ cm$ whose density is twice that of the outer portion. If this cube is just floating in a liquid of density $2\ g/cm^3$, find the density of the inner portion
Medium
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$m g=2 \rho_{1} \times 10^{3}+\rho_{1} \times\left(20^{3}-10^{3}\right)$
$=9 \rho_{1} \times 10^{3} \mathrm{g}=\rho \times 8 \times 10^{3} \mathrm{g}$
$\Rightarrow \rho_{1}=\frac{8}{9} \mathrm{gm} / \mathrm{cc}$
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