Mechanical Properties of Fluids

A cylindrical tube, with its base as shown in the figure., is filled with water. It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta=45^{\circ}$. $P_{1}$ and $P_{2}$ are…

As shown schematically in the figure, two vessels contain water solutions (at temperature $T$) of potassium permanganate $(KMnO_{4})$ of different concentrations $n_{1}$ and $n_{2}(n_{1}>n_{2})$ molecules per unit…

An open-ended U-tube of uniform cross-sectional area contains water (density $10^{3}kgm^{-3}$ ). Initially the water level stands at $0.29m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of…

A cylindrical capillary tube of $0.2mm$ radius is made by joining two capillaries $T_{1}$ and $T_{2}$ of different materials having water contact angles of $0^{o}$ and $60^{o},$ respectively. The capillary tube is…

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant…

A spherical body of radius $R$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $P(r)$ is the pressure at $r(r<R)$ , then the correct option(s) is (are)

Two spheres $P$ and $Q$ of equal radii have densities $\rho_{1}$ and $\rho_{2}$ , respectively. The spheres are connected by a massless string and placed in liquids $L_{1}$ and $L_{2}$ of densities $\sigma_{1}$ and…

Paragraph: A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the…

Paragraph: A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the…

A glass capillary tube is of the shape of a truncated cone with an apex angle $\alpha$ so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height $h$,…

A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3 ρ The complete…

Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as…