Embibe Experts Solutions for Chapter: Fluid Mechanics, Exercise 3: Exercise - 3

Statement-$1$: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

Statement-$2$: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

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 shown in the figure with a tension in the string. The arrangement is possible only if

A solid sphere of radius $R$ and density $\rho$ is attached to one end of massless spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete arrangement is placed in a liquid of density $2\rho$ and is allowed to reach equilibrium. The correct statement (s) is (are)

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance $d=1.2 \mathrm{m}$ from the person. In the following, the state of the lift's motion is given in $\mathrm{List}-\mathrm{I}$ and the distance where the water jet hits the floor of the lift is given in $\mathrm{List}-\mathrm{II}.$ Match the statements from $\mathrm{List}-\mathrm{I}$with those in $\mathrm{List}-\mathrm{II}$ and select the correct answer using the code given below lists.

A jar is filled with two non-mixing liquids $1$ and $2$ having densities ${\mathrm{\rho }}_1$ and ${\rho }_2$ respectively. A solid ball, made of a material of density ${\mathrm{\rho }}_3,$ is dropped in the jar. It comes to equilibrium in the position shown in the figure.

Which of the following is true for ${\mathrm{\rho }}_1, {\mathrm{\rho }}_2$ and ${\rho }_3$?

A ball is made of a material of density $\mathrm{\rho }$ where ${\mathrm{\rho }}_{\mathrm{oil}} <\mathrm{\rho }<{\mathrm{\rho }}_{\mathrm{water}}$ with ${\mathrm{\rho }}_{\mathrm{oil}}$ and ${\mathrm{\rho }}_{\mathrm{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

Water is flowing continuously from a tap having an internal diameter $8 \times {10}^{–3} \mathrm{m}$. The water velocity as it leaves the tap is $0.4 \mathrm{m} {\mathrm{s}}^{–1}$. The diameter of the water stream at a distance $2 \times {10}^{–1} \mathrm{m}$ below the tap is close to:

A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, form a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is