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

A U-tube in which the cross-sectional area of the limb on the left is one-quarter, the limb on the right contains mercury (density $13.6\mathrm{ }\mathrm{g} {\mathrm{cm}}^{-3}$). The level of mercury in the narrow limb is at a distance of $36\mathrm{ }\mathrm{cm}$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?