Physics - Fluid Question with Solution | TestHub

Due to its higher density, cold water stays close to the bottom of a rectangular vessel which is filled up to the height of $\mathrm{h}=30\mathrm{cm}$. We assume that the density of water in the vessels grows linearly with increasing depth - at the water level, the density is equal to ${\rho }_1=996\mathrm{kg}\cdot {\mathrm{m}}^{-3}$, while the density ${\rho }_{\mathrm{b}}$ at the bottom of the vessel is unknown. Determine this density using the fact, that a homogeneous rod with density ${\rho }_{\mathrm{r}}=997\mathrm{kg}\cdot {\mathrm{m}}^{-3}$ and length h immersed in the water and fixed by one of its ends at the water level makes an angle of $\phi =60^{\circ }$ with the vertical. Fill value of x in OMR if ${\rho }_{\mathrm{b}}=996+\mathrm{x}$