Mechanical properties of fluids practice · Mixed difficulty

In a turbulent flow, the velocity of the liquid in contact with the walls of the tube is

The length of a needle floating on water is $2.5 \mathrm{~cm}$. How much minimum force, in addition to the weight of the needle, will be needed to lift the needle above the surface of water? Surface tension of water $=7.2 \times 10^{-4} \mathrm{~Ncm}^{-1}$.

At what speed will the velocity head of stream of water be $40 \mathrm{~cm}$?

Express standard atmospheric pressure in torr.

Bernouli's equation is valid for

A jeweller claims that he sells ornaments made of pure gold that has the relative density of $19.3.$ He sells a necklace weighing $25.250 \mathrm{~g f}$ to a person. The clever customer weighs the necklace when immersed in pure water and finds that it weighs $23.075 \mathrm{~g f}$ in water. Is the ornament made of pure gold?

A soap bubble has radius $'r'$. What will be the value of work done if its radius increases to three times of initial value without changing temperature (surface tension of soap solution is $'T'$)

Statement-A: Mosquitos are killed (which are present in water) when kerosene is sprayed on water surface in tanks or ponds.
Statement-B: Kerosene is very harmful for mosquitoes.

The potential energy of molecule on the surface of a liquid compared to one inside the liquid is

A drop of water of volume $V$ is pressed between the two glass plates so as to spread to an area $A$. If $S$ is the surface tension, then normal force required to separate the glass plates is

$\mathbf{A}$ : An iron needle placed carefully on the surface of water may float, whereas a solid ball of same material will always sink

$\mathbf{R}$ : The buoyancy on an object depends both on the material and shape of object.

Scent sprayer is based on

Which of the following statement(s) is/are correct?

I. An ice ball is floating in water. Some stone pieces are embedded inside the ice. When ice will melt, level of water will fall.

II. In floating condition, stone pieces will displace more liquid compared to the condition when they sink.

A ball of mass $m$ and radius $r$ is gently released in a viscous liquid. The mass of the liquid displaced by it is ${m}^{\prime}$, such that $m > m^{\prime}$. The terminal velocity is proportional to

A small tiny lead shot is gently dropped on the surface of a viscous liquid

A hollow cylinder of mass $m$ made heavy at its bottom is floating vertically in water. It is tilled from its vertical position through an angle $\theta$ and is left. The restoring force acting on it is

Excess pressure inside a liquid drop of radius $R$ is $P_1$ and inside a bubble of same liquid and same radius $R$ is $P_2$ then $P_1: P_2$ is

The cylindrical tube of a spray pump has a crosssection of $8.0 \mathrm{~cm}^2$, one end of which has 40 fine holes each of diameter $1.0 \mathrm{~mm}$. If the liquid flow inside the tube is $1.5 \mathrm{~m} \mathrm{~min}^{-1}$, what is the speed of ejection of the liquid through the holes?

Statement A: Aero planes are made to run on the runway before take off, so that they acquire the necessary lift.
Statement B: According to Bernoulli's theorem, as velocity increases pressure decreases and vice versa.

A suction pump at ground level can draw water from a well whose depth of level is:

Statement-1: When a drop of ink falls on a news paper, it spreads on it.
Statement-2: Adhesive force between ink and paper is greater than cohesive force between ink molecules.

Water rises up in a glass capillary upto a height of $9.0 \mathrm{~cm}$, while mercury falls down by $3.4 \mathrm{~cm}$ in the same capillary. Assume angles of contact for water-glass and mercury-glass as $0^{\circ}$ and $135^{\circ}$ respectively. Determine the ratio of surface tensions of mercury and water. Take $\cos 135^{\circ}=-0.71.$

A metallic wire of diameter '$d$' is lying horizontally on the surface of water. The maximum length of wire so that it may not sink will be

Assertion: When fluids flow, there is some loss of energy due to friction.
Reason: Different layers of the fluid exert forces on each other.

Choose the correct statement

Consider the two statements:
Statement-1: A capillary tube is frst dipped in hot water and then dipped in cold water. The rise is higher in hot water.
Statement-2: Capillary tube is first dipped in cold water and then dipped in hot water. The rise is higher in cold water.

Assertion: The flow is streamline for Reynolds number less than 2000.
Reason: The flow of liquid is unstable for Reynolds number greater than 3000.

Statement A: The shape of an automobile is so designed that its front resembles the stream line pattern of the fluid through which it moves.
Statement B: The resistance offered by the fluid is maximum.

On which of the following, the terminal velocity of a solid ball in a viscous fluid is independent?

An air bubble of radius $1 \mathrm{~mm}$ is formed inside water at a depth $10 \mathrm{~m}$ below free surface (where, air pressure is $10^5 \mathrm{Nm}^{-2}$ ). The pressure inside the bubble is (surface tension of water $=7 \times 10^{-2} \mathrm{Nm}^{-1}$ )