Mechanical Properties of Fluids

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 $10m$ as shown in figure. Each liquid has a height of $5m.$ The ratio of the forces…

A hydraulic press can lift $100\mathrm{kg}$ when a mass $m$is placed on the smaller piston. It can lift kg when the diameter of the larger piston is increased by $4$ times and that of the smaller piston is decreased by…

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095 \mathrm{~J} / \mathrm{m}^2$ and density $10^3 \mathrm{~kg} / \mathrm{m}^3$. The difference…

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0\mathrm{cm}^{2}$. The area of cross section at the outlet is $10\mathrm{mm}^{2}$. If the piston is pushed at a speed…

A drop of liquid of density $\rho\,$is floating half immersed in a liquid of density $\sigma\,$and surface tension $7.5\times\,10^{-4}N\mathrm{cm}^{-1}$. The radius of drop in $\mathrm{cm}$will be : (Take :…

A metal block of base area $0.20m^{2}$ is placed on a table, as shown in figure. A liquid film of thickness $0.25\mathrm{mm}$ is inserted between the block and the table. The block is pushed by a horizontal force of…

On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the…

A small spherical droplet of density $d$ is floating exactly half immersed in a liquid of density $\rho\,$ and surface tension $T.$ The radius of the droplet is (take note that the surface tension applies an upward…

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $10 \mathrm{~N}$ is applied on the surface of water in the thinner arm. The force required to be applied on the…

Consider a water tank as shown in the figure.It's cross-sectional area is $0.4m^{2}$. The tank hasan opening $B$ near the bottom whose cross-section area is $1\mathrm{cm}^{2}$. A load of $24\mathrm{kg}$ is applied on…

A square hole of side length $\ell$ is made at a depth of $\mathrm{h}$ and a circular hole of radius $\mathrm{r}$ is made at a depth of $4 \mathrm{~h}$ from the surface of water in a water tank kept on a horizontal…

A soap bubble of the radius $3\mathrm{cm}$ is formed inside another soap bubble of radius,$6\mathrm{cm}$. The radius of an equivalent soap bubble that hasthe same excess pressure as inside the smaller bubble with…