Mechanical properties of fluids practice · Medium

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

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 $=7 \times 10^{-2} \mathrm{Nm}^{-1}$ )

Streamline flow is more likely for liquid with

Assertion:- Surface tension of water is larger among fluids.
Reason:- There is hydrogen bond in water molecule so its surface tension is larger than other fluids.

A block weighs $15 \mathrm{~N}$ in air. It weighs $12 \mathrm{~N}$ when immersed in water. When immersed in another liquid, it weighs $13 \mathrm{~N}$. Calculate the relative density (specific gravity) of the other liquid.

A raft of wood of mass $120 \mathrm{~kg}$ floats in water. The weight that can be put on the raft to make it just sink, should be (Take, $d_{\text {raft }}=600 \mathrm{kgm}^{-3}$ )

A drop of liquid of diameter 2.8 mm breaks up into 125 identical drops. The change in energy is nearly $\left( {S = 75\,\,\mathrm{dyne}\,\,\mathrm{c}{\mathrm{m}^{ - 1}}} \right)$

The amount of work done in blowing a soap bubble such that its diameter increases from d to $D$ is ($S =$surface tension of solution)

A beaker containing water is balance on the pan of a common balance. A solid of specific gravity 1 and mass 5 g is tied to the arm of the balance and immersed in water contained in the beaker. The scale pan with the beaker

Pressure inside a liquid drop is greater than the pressure outside by an amount $\frac{2 S}{R},$ where $S$ is surface tension of liquid and $R$ is radius of liquid drop. When 8 such identical drops combine together become one single drop than the pressure difference between inside and outside the drop will be

A cubical block of ice floating in water has to support a metal piece weighing $0.5 \mathrm{~kg}$. What can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice $=0.9.$

If the excess pressure inside a liquid drop is 3 times of excess pressure of another liquid drop made from same liquid. Find ratio of their volumes.

The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of soap bubble, the work done in doing so is given by

A rain drop of radius 0.3 mm has a terminal velocity in air = 1 m/s. The viscosity of air is $8 \times {10^{ - 5}}$ poise. The viscous force on it is

Statement I: Finer the capillary, greater is the height to
which the liquid rises in the tube.

Statement II: This is in accordance with the ascent
formula.

The excess of pressure inside the first soap bubble is $\sqrt{3}$ times that inside the second bubble. The ratio of volume of the first to that the second bubble is