A piece of solid weighs $120 \mathrm{gm}$ in open air, $90 \mathrm{gm}$ in water and $60 \mathrm{gm}$ in a liquid. The relative density of solid and that of liquid are respectively.

Water stands upto height $\text{'}h\text{'}$ behind the dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. Density of water is $\text{'}\rho \text{'}$ and acceleration due to gravity is $\text{'}g\text{'}$. If atmospheric pressure force is also considered, the point of application of total force acting on the dam due to water above $\text{'}o\text{'}$ is_____

A barometer is constructed using a liquid (density $=760 \mathrm{kg} {\mathrm{m}}^{-3}$). What would be the height of the liquid column, when a mercury barometer reads $76 \mathrm{cm}?$

(density of mercury $=13600 \mathrm{kg} {\mathrm{m}}^{-3}$)

The liquid shown in the figure in the two arms is mercury (specific gravity $13.6$) and water. If the difference of heights of the mercury column is $2 \mathrm{cm}$, the height $h$ of the water column is

An open-ended U-tube of uniform cross-sectional area contains water (density ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ ). Initially the water level stands at $0.29 \mathrm{m}$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 \mathrm{kg} {\mathrm{m}}^{-3}$ is added to the left arm until its length is $0.1 \mathrm{m}$, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is

A cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density ${\rho }_{\mathit{w}}$ ) and its neck is filled with immiscible oil (density ${\rho }_0$). Then the pressure at;