The diagram shows venturi meter through which water is flowing. The speed of water at $X$ is $2\mathrm{c}\mathrm{m}/\mathrm{s}$. Find the speed of water at $Y$ in $\mathrm{c}\mathrm{m}/\mathrm{s}$. (taking $g=1000\mathrm{c}\mathrm{m}/{\mathrm{s}}^2$).

In the figure shown, the heavy cylinder (radius, $\sqrt{\frac{8}{3}}\mathrm{m}$) kept on a smooth surface separates two liquids of densities $2\rho$ and $3\rho$. The height $h$ (in meter) for the translational equilibrium of the cylinder must be

For the system shown in the figure, the cylinder on the left at $L$ has a mass of $600\mathrm{k}\mathrm{g}$ and a cross sectional area of $800\mathrm{c}{\mathrm{m}}^2$. The piston on the right, at $S$, has cross sectional area $25\mathrm{c}{\mathrm{m}}^2$ and negligible weight. If the apparatus is filled with oil $(\rho =0.75\mathrm{g}/\mathrm{c}{\mathrm{m}}^3)$ Find the force $F$ (in $\mathrm{N}$) required to hold the system in equilibrium. Take $g=10\mathrm{m}/{\mathrm{s}}^2$.

A siphon has a uniform circular base of diameter $\frac{8}{\sqrt{\pi }}\mathrm{c}\mathrm{m}$ with its crests $1.8\mathrm{m}$ above water level as shown in figure. Find absolute pressure at the crest level $A$ (in $kPa$). [Use $P_0={10}^5\mathrm{N}/{\mathrm{m}}^2$ and $g=10\mathrm{m}/{\mathrm{s}}^2$]

A uniform rod of length $b=90\mathrm{c}\mathrm{m}$ capable of turning about its end which is out of water, rests inclined to the vertical. If its specific gravity is $5/9$, find the length immersed in water (in $\mathrm{c}\mathrm{m}$).