The figure shows a quarter cylindrical dam surface retaining water. The density of water is $1000\mathrm{ }\mathrm{kg} {\mathrm{m}}^{-2}$. The length of the dam normal to paper is $=30\mathrm{ }\mathrm{m}.$ Determine the horizontal and vertical components of the force due to water on the dam.

A hemispherical gate of radius $R$ is just submerged in water of density $\rho$ as shown in figure. Find the thrust on the gate due to water in horizontal direction? Do not count atmospheric pressure.

A hemispherical gate of radius $R$ is just submerged in water of density $\rho$ as shown in figure. Find the thrust on the gate due to water in vertical direction?

A hemispherical gate of radius $R$ is just submerged in water of density $\rho$ as shown in figure. Calculate total hydrostatic force acting on gate.

A hemispherical gate of radius $R$ is just submerged in water of density $\rho$ as shown in figure. Calculate angle of orientation of total hydrostatic force acting on the hemispherical gate. Do not count atmospheric pressure.

An open pan $P$ filled with water (density ${\text{ρ}}_{\mathrm{w}}$ ) is placed on a vertical rod, maintaining equilibrium, A block of density $\text{ρ}$ is placed on one side of the pan as shown. Water depth is more than height of the block.

A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration $a$ towards right (ignore effect of gravity). Pressure is $\left(i\right)$ maximum at, and $\left(ii\right)$ minimum at :

A vertical U-tube of uniform inner cross-section contains mercury in both sides of its arms. A glycerin $(\text{density}=1.3\mathrm{ }\mathrm{g} {\mathrm{cm}}^{-3})$ column of length $10\mathrm{ }\mathrm{cm}$ is introduced into one of its arms. Oil of density $0.8\mathrm{ }\mathrm{gm} {\mathrm{cm}}^{-3}$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column. Density of mercury $=13.6\mathrm{ }\mathrm{g} {\mathrm{cm}}^{-3}$.

A triangular lamina of area $A$ and height $h$ is immersed in a liquid of density $\text{ρ}$ in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is