A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000 \mathrm{kg}$. The area of cross-section of the piston carrying the load is $425 {\mathrm{cm}}^2$. What maximum pressure would the smaller piston have to bear?

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_____

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

A cylindrical block of wood (density = $650 \mathrm{kg} {\mathrm{m}}^{-3}$), of base area $30\mathrm{ }{\mathrm{cm}}^2$ and height $54 \mathrm{cm}$, floats in a liquid of density $900 \mathrm{kg} {\mathrm{m}}^{-3}$. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :

Two liquids of densities ${\rho }_1$ and ${\rho }_2\left({\rho }_2=2{\rho }_1\right)$ are filled up behind a square wall of side $10 \mathrm{m}$ as shown in figure. Each liquid has a height of $5 \mathrm{m}.$ The ratio of the forces due to these liquids exerted on upper part $MN$ to that at the lower part $NO$ is (Assume that the liquids are not mixing):

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is $5 \mathrm{cm}$ and the angular speed of rotation is $\mathrm{\omega } \mathrm{rad} {\mathrm{s}}^{-1}$. The difference in the height, $\mathrm{h} \left(\mathrm{in} \mathrm{cm}\right)$ of liquid at the Centre of vessel and at the sides of the vessel will be :