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Question 11 Mark
Fill in the blanks using the word (s) from the list appended with statement: For solids with elastic modulus of rigidity, the shearing force is proportional to . . . while for fluids it is proportional to . . . (shear strain/ rate of shear strain).
Answer
For solids with elastic modulus of rigidity, the shearing force is proportional to shear strain while for fluids it is proportional to rate of shear strain. With reference to the elastic modulus of rigidity for solids, the shearing force is proportional to the shear strain. With reference to the elastic modulus of rigidity for fluids, the shearing force is proportional to the rate of shear strain.
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Question 21 Mark
A tank with a square base of area $1.0 \mathrm{~m}^2$ is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area $20 \mathrm{~cm}^2$. The tank is filled with water in one compartment, and an acid (of relative density 1.7 ) in the other, both to a height of 4.0 m . compute the force necessary to keep the door close.
Answer
Water compartment, $\mathrm{p}=\mathrm{hpg}=4 \times 1.0 \times 109 \times 9.8$
$=39.2 \times 10 \mathrm{~Pa}$
Acid compartment, $\mathrm{P}=\mathrm{hp}$ 's
$=4 \times 1.7 \times 103 \times 9.8$
$=66.64 \times 10 \mathrm{~Pa}$
$\mathrm{P}^{\prime}-P=66.64 \times 103-39.2 \times 10^3$
$=27.44 \times 10^3 \mathrm{~Pa}$
$A=20 \mathrm{~cm}$
$20 \times 10^{-4} \mathrm{~m}^2$
Area, using pressure, $\mathbf{P}=\frac{\mathrm{F}}{\mathrm{A}}$
$\mathrm{F}=\mathrm{PA}$
$\mathrm{~F}=\left(20 \times 10^{-4}\right) \times\left(27.44 \times 10^3\right)$
$=54.88 \mathrm{~N}$
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Question 31 Mark
During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000Pa. At what height must the blood container be placed so that blood may just enter the vein? [Use the density of whole blood from Table 10.1].
Answer
pressure, P = 2000Pa Density of whole blood, $\rho=1.06\times^3\text{kg m}^{-3}$ Acceleration due to gravity, $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$ Height of the blood container = h Pressure of the blood container, P = hpg $\therefore\text{h}=\frac{\text{P}}{\rho\text{g}}$ $=\frac{2000}{1.06\times^3\times9.8}$ $=0.1925\text{m}$ The blood may enter the vein if the blood container is kept at a height greater than 0.1925m, i.e., about 0.2m.
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Question 41 Mark
Fill in the blanks using the word (s) from the list appended with statement: For a fluid in steady flow, the increases inflow speed at a constriction follows from…… while the decrease of pressure there follows from….....(conservation of mass/ Bernoulli’s principle).
Answer
For a fluid in steady flow, the increases inflow speed at a constriction follows from conservation of mass while the decrease of pressure there follows from Bernoulli's principle. For a steady-flowing fluid, an increase in its flow speed at a constriction follows the conservation of mass/ Bernoulli's principle.
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Question 51 Mark
Fill in the blanks using the word (s) from the list appended with statement: Viscosity of gases . . . with temperature, whereas viscosity of liquids . . . with temperature. (increases/ decreases)
Answer
Viscosity of gases Increases with temperature, whereas viscosity of liquids decreases with temperature. Most fluids offer resistance to their motion. This is like internal mechanical friction, known as viscosity. Viscosity of gases increases with temperature, while viscosity of liquids decreases with temperature.
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Question 61 Mark
Explain why When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers.
Answer
By doing so the area of outlet of water jet is reduced, so velocity of water increases according to equation of continuity, Area × Velocity = Constant.
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Question 71 Mark
Fill in the blanks using the word(s) from the list appended with statement: Surface tension of liquids generally . . . with temperatures. (increases/ decreases)
Answer
Surface tension of liquids generally decreases with temperatures. The surface tension of a liquid is inversely proportional to temperature.
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Question 81 Mark
Explain why Atmospheric pressure at a height of about 6km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100km.
Answer
Density of air is the maximum near the sea level. Density of air decreases with increase in height from the surface. At a height of about 6km, density decreases to nearly half of its value at the sea level. Atmospheric pressure is proportional to density. Hence, at a height of 6km from the surface, it decreases to nearly half of its value at the sea level.
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Question 91 Mark
Fill in the blanks using the word (s) from the list appended with statement: For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater/ smaller).
Answer
For the model of a plane in a wind tunnel, turbulence occurs at a Greater speed for turbulence for an actual plane (greater/ smaller). For the model of a plane in a wind tunnel, turbulence occurs at a greater speed than it does for an actual plane. This follows from Bernoulli's principle and different Reynolds' numbers are associated with the motions of the two planes.
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Question 101 Mark
What is the work done in blowing a soap bubble of radius 'r and surface tension $'\sigma'?$
Answer
Work done = S.T. area of soap bubble$=\sigma\times(4\pi\text{r}^2)\times2=8\pi\text{r}^2$
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Question 111 Mark
Water flows faster than honey. Why?
Answer
Coefficient of viscosity n is less as compared to the value of honey. So, water flows faster than honey.
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Question 121 Mark
Why does the cotton wick in an oil filled lamp keep on burning?
Answer
In the cotton wick, there are very large number of capillaries in which oil continues to rise.
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Question 131 Mark
What is pitot tube? State the principle on which it is based.
Answer
It is a simple device which is used for measuring the velocity of the flow at any depth in a flowing liquid. It is based on Bernoulli's theorem.
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Question 141 Mark
When two soap bubbles stay in contact, what is the radius of the interface?
Answer
If $\text{r}_1$ and $\text{r}_2$ are the radii of the soap bubbles, the net excess pressure at the interface is,$\frac{4\sigma}{\text{r}_{\text{eq}}}=\frac{4\sigma}{\text{r}_1}-\frac{4\sigma}{\text{r}_2}$
$\therefore\frac{1}{\text{r}_\text{eq}}=\frac{1}{\text{r}_1}-\frac{1}{\text{r}_2}$
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Question 151 Mark
Why the aeroplanes and cars are given a streamline shape?
Answer
This is done to reduce the backward drag of the atmosphere.
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Question 171 Mark
Surface tension of all lubricating oils and paints is kept low. Why?
Answer
In order to have low value of surface tension so that it can spread over large area.
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Question 181 Mark
When air is blown in between two balls suspended close to each other, they are attracted towards each other. Give reason.
Answer
When air is blown in between two balls suspended close to each other with high speed, a low pressure is created between the balls which is much less than the atmospheric pressure beyond the balls. Due to this, balls are attracted towards each other. This is according to Bernoulli's theorem.
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Question 191 Mark
A mercury barometer is placed in the mercury trough in a way that the angle made with the vertical is 60°. Find the height of mercury column.
Answer
The height of mercury in the inclined case will be 76cm.
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Question 201 Mark
If a mercury barometer is fitted such that the angle made with the vertical is 30°, what will be the height of mercury column under one atmosphere?
Answer
Under normal conditions, it will be 76cm of vertical column. So, the height of mercury in the slant length has to be 76cm.
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Question 211 Mark
Why is it that a liquid set in rotation comes to rest after some time?
Answer
The liquid comes to rest due to the viscous force i.e., due to internal fluid friction between its different layers.
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Question 241 Mark
Does Archimedes' principle hold in a vessel in free fall or in a satellite moving in a circular orbit?
Answer
No.
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Question 251 Mark
Three vessels have same base area and different neck area. Equal volume of liquid is poured into them, which will possess more pressure at the base?
Answer
If the volumes are same, then height of the liquid will be highest in which the cross-sectional area is least at the top. So, the vessel having least cross-sectional area at the top possess more pressure at the base $\because(\text{P}=\rho\text{gh})$
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Question 261 Mark
What are the values of Reynolds number ($N_R$) for different types of flows?
Answer
For streamline or laminar flow $0<N_R<2000$, For turbulent flow, $N_R>3000$ If N, lies between 2000 to 3000 , the flow is unstable i.e., change from streamline flow to turbulent flow.
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Question 271 Mark
A block of wood is floating in a lake. What is apparent weight of the floating block?
Answer
The apparent weight of the floating block is equal to zero because the weight of the block acting vertically downwards is balanced by the buoyant force acting on the block upwards.
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Question 291 Mark
What happens to surface tension, when impurity is mixed in liquid?
Answer
Surface tension of the liquid decreases.
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Question 301 Mark
What is $(i)$ velocity head $(ii)$ pressure head?
Answer
  1. $\frac{\upsilon^2}{2\text{g}}$
  2. $\frac{\text{P}}{\rho\text{g}}$
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Question 311 Mark
A square framed with a wire of side 'L' is dipped in a liquid. On taking out, a membrane is formed. What will be the force acting on the frame if the surface tension of liquid is S?
Answer
The membrane has two surfaces. Force on frame due to surface tension = 8SL.
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Question 321 Mark
Why is the dam of water reservoir thick at the bottom?
Answer
It is so because the pressure of water in reservoir increases with depth.
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Question 341 Mark
Why does the liquid level stay higher below the point B?
Answer
Due to increased velocity in the lesser cross-sectional area, the pressure will be less as there exists a streamlined flow.
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Question 351 Mark
What is the excess pressure in a soap bubble of radius 10mm, if surface tension is $2.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$?
Answer
In a soap bubble, excess pressure $=\text{P}=\frac{4\sigma}{\text{r}}$$\therefore\text{P}=\frac{4\times2.5\times10^2}{10\times10^{-3}}=10\text{Nm}^{-2}$
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Question 361 Mark
A tank with a square base of area $1.0 \mathrm{~m}^2$ is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area $20 \mathrm{~cm}^2$. The tank is filled with water in one compartment, and an acid (of relative density 1.7 ) in the other, both to a height of 4.0 m . compute the force necessary to keep the door close.
Answer
Water compartment, $p=h p g=4 \times 1.0 \times 109 \times 9.8$
$=39.2 \times 10 \mathrm{~Pa}$
Acid compartment, $\mathrm{P}=\mathrm{hp}$ 's
$=4 \times 1.7 \times 103 \times 9.8$
$=66.64 \times 10 \mathrm{~Pa}$
$P^{\prime}-P=66.64 \times 103-39.2 \times 10^3$
$=27.44 \times 10^3 \mathrm{~Pa}$
$A=20 \mathrm{~cm}$
$20 \times 10^{-4} \mathrm{~m}^2$
Area, using pressure, $\mathrm{P}=\frac{\mathrm{F}}{\mathrm{A}}$
$\mathrm{F}=\mathrm{PA}$
$\mathrm{~F}=\left(20 \times 10^{-4}\right) \times\left(27.44 \times 10^3\right)$
$=54.88 \mathrm{~N}$
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Question 371 Mark
Show the variation of pressure in the atmosphere with height in km. Considering that the density of air is not dependent on pressure.
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Question 381 Mark
Why the speed of a whirl wind in a tornado is alarmingly high?
Answer
Due to reduction in moment of inertia, angular velocity increases to keep the angular momentum constant.
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Question 391 Mark
A container of area $0.02m^2$ is filled with water. Find the pressure at the bottom of the container if a weight is placed on the piston. (as shown in the figure).
Answer

The net force acting on the base,$=(\rho\text{gh})\text{A}+\text{mg}$
$\text{F}=1000\times9.8\times1\times0.02+10\times9.8$
$=294\text{N}$
$\therefore$ Pressure $=\frac{\text{Trust}}{\text{Area}}=\frac{294\text{N}}{0.02}=14700\text{N}$
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Question 401 Mark
What is the impact on surface tension when $(i)$ impurity is increased, and $(ii)$ temperature is decreased?
Answer
Surface tension:
  1. Reduces with increasing impurity.
  2. Increases with decrease in temperature.
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Question 411 Mark
A steel ball is floating in a trough of mercury. If we fill the empty part of the trough with water, what will happen to the steel ball?
Answer
It will move up.
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Question 421 Mark
Under which condition $(i)$ the centre of buoyancy coincides with the centre of gravity $(ii)$ the centre of buoyancy does not coincide with the centre of gravity.
Answer
  1. For a solid body of uniform density, the centre of gravity coincides with the centre of buoyancy.
  2. For a solid body having different densities over different parts, its centre of gravity does not coincide with the centre of buoyancy.
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Question 431 Mark
What is the effect of gravity on pressure?
Answer
Pressure increases as it is proportional to the depth we move into a liquid due to the weight of the liquid between the two layers.
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Question 441 Mark
Why do fire fighters have a jet attached to the head of their water pipes?
Answer
This is done to increase the velocity of water flowing out of the pipe.
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Question 451 Mark
Can two streamlines cross each other in a flowing liquid?
Answer
No, two streamlines cannot cross each other.
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Question 461 Mark
Why water cannot be poured into a bottle with a narrow neck with the aid of glass tube?
Answer
The pressure of air inside the bottle and the adhesive force between water and glass do not permit the water to get filled in the bottle with narrow neck.
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Question 471 Mark
What is the use of open tube manometer?
Answer
Open tube manometer is used for measuring pressure difference.
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Question 481 Mark
During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000Pa. At what height must the blood container be placed so that blood may just enter the vein? [Use the density of whole blood from Table 10.1].
Answer
pressure, P = 2000Pa Density of whole blood, $\rho=1.06\times^3\text{kg m}^{-3}$ Acceleration due to gravity, $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$ Height of the blood container = h Pressure of the blood container, P = hpg$\therefore\text{h}=\frac{\text{P}}{\rho\text{g}}$
$=\frac{2000}{1.06\times^3\times9.8}$
$=0.1925\text{m}$
The blood may enter the vein if the blood container is kept at a height greater than 0.1925m, i.e., about 0.2m.
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Question 491 Mark
Why a hot liquid moves faster than a cold liquid?
Answer
Due to decrease in viscosity with increase of temperature.
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Question 511 Mark
Three containers have different area on the top surface and same base area. If equal volume of a liquid is put in them which will have more pressure at its base?
Answer
For equal volume, the vertical height of the liquid in the container will be more if the cross-section reduces at the top. So, pressure at the bottom of the container with less area is more.
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Question 531 Mark
Why does mercury drop its level in a capillary tube?
Answer
Excess pressure always acts on the concave side and for mercury there is upper convex surface. So, it drops its level in capillary tube.
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Question 541 Mark
It becomes easier to spray the water in which some soap is dissolved, explain it.
Answer
When some soap is dissolved in water, the surface tension of water decreases. Thus, the less energy required to spray water.
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Question 551 Mark
What is the relation for maximum range of water coming out from an orifice on the side wall of a tank?
Answer
Maximum range $=2\sqrt{\text{h}(\text{H}-\text{h})},$ where h is the depth from top surface at which the hole is.
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Question 561 Mark
If you double the radius of the capillary tube, what will be the drop in height rise in the tube?
Answer
For the same liquid, hr = constant$\therefore$ Doubling the radius makes the height half.
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Question 571 Mark
The height of water level in a tank is H = 96cm. Find the range of water stream coming out of a hole at depth $\frac{\text{H}}4$ from upper surface of water.
Answer
The depth of hole below the upper surface of water is,$\text{h}=\frac{\text{H}}{4}=\frac{96}{4}=24\text{cm}$
THe height of hole from ground is,$\text{h}'=96-24=72\text{cm}$
Horizontal range $=2\sqrt{\text{hh}'}$$=2\sqrt{24\times72}=48\sqrt3\text{cm}$
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Question 581 Mark
The bags and suitcases are provided with broad handles. Why?
Answer
So that small pressure is exerted while carrying them.
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Question 591 Mark
This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
Answer
Temperature (T) remains constant only near the surface of the earth not at greater height.
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Question 601 Mark
What is the cause far velocity gradient as a liquid flows in a tube of radius ‘r' with its velocity along the axis being 'v’?
Answer
A velocity gradient of “v/ r” is seen in the tube due to the phenomenon of viscosity.
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Question 611 Mark
Why does a soft plastic bag weigh the same when empty as when filled with air at atmospheric pressure?
Answer
Actually the weight of plastic bag when filled with air pressure is more than when it is empty. The increase in weight equals the buoyant force due to air, so the bag weighs the same.
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Question 621 Mark
Why do the asbestos roof of houses get lifted in hurricane?
Answer
Due to high velocity of air outside the house, the pressure inside becomes more than outside. So, it rises up.
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Question 631 Mark
Why is the dome of water reservoir thick at the bottom?
Answer
It is so because the pressure of water in reservoir increases with depth.
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Question 641 Mark
When can liquid be in equilibrium?
Answer
A liquid can be in equilibrium, if:
  1. Only normal forces act on it.
  2. The pressure at all points in a surface remains constant.
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Question 651 Mark
Why does a hot liquid move faster than cold liquid?
Answer
A hot liquid moves faster than cold liquid because the viscosity of liquid decreases with the increase in temperature.
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Question 661 Mark
What is gauge pressure?
Answer
The difference between absolute pressure and atmospheric pressure is known as gauge pressure. As, $\text{P}_{\text{absolute}}=\text{P}_\text{a}+\rho\text{gh}$ So, $\text{P}_{\text{absolute}}\ -\text{P}_\text{a}=\rho\text{gh}$ i.e. $\text{P}_\text{gauge}=\rho\text{gh}$ Here, $\rho$ is the density of a fluid of depth h.
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Question 671 Mark
Surface tension of all lubricating oils and paints is kept low. Why?
Answer
Low value of surface tension has been kept for paints and oils so that it can spread over large area.
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Question 681 Mark
Why is it that the smaller bubbles have a greater excess pressure?
Answer
Excess pressure is inversely proportional to the radius.
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Question 691 Mark
What is effect on the equilibrium of a physical balance when air is blown below one pan?
Answer
When air is blown below one pan, there will be increase in air velocity and due to which the pressure drops there. Hence, the pan goes down.
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Question 701 Mark
When a shaving brush is taken out of water its hairs cling together. Why?
Answer
Due to surface tension, the water film formed in between the hairs that tends to make the surface area minimum. As a result of which the hairs of shaving brush come close to each other.
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Question 711 Mark
A glass plate of length $10\ cm$, breadth $4\ cm$ and thickness $0.4\ cm$ weighs $20g$ in air. It is held vertically with long side horizontal and half the plate immersed in water. What will be its apparent weight? Surface tension of water $= 70 dyne/cm.$
Answer
Here,$ l = 10\ cm; b = 4\ cm; t = 0.4\ cm; m = 20g;\sigma=70\text{dyne/cm,}$ App. weight $=$ ?
The various forces acting on the plate are as follows:
  1. Weight of the acting vertically downards,
$= mg = 20 \times 980\  dyne$
$= 20\ gf$
  1. Force due to surface tension acting vaertically downwards,
$\text{F}=\sigma\times$ length of plate in contact with water
$=\sigma\times ($length $+$ thickness$) \times 2$
$= 70 \times (10 + 0.4) \times 2$
$= 70 \times 20.8\  dyne$
$=\frac{70\times20.8}{980}\text{gf}=1.4857\text{gf}$
  1. Upwards thrust due to liquid $=$ weight of the liquid displaced by the body
$= ($Volume displaced$) \times$ Density $\times g$
$=\Big(\frac{\text{l}\times\text{b}}{2}\times\text{t}\Big)\times\rho\times\text{g}$
$=\Big(10\times\frac42\times0.4\Big)\times1\times980\ \text{dyne}$
$=\frac{8\times980}{980}\text{gf}=8\text{gf}$
$\therefore$ Apparent weight
$= 20 + 1.4857 - 8 = 13.4857\ gf$
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Question 731 Mark
When 200g mass placed in a cylindrical beaker of base area 'a' is removed, the vertical length comes out of water by 2cm. What is the radius of the cylinder?
Answer
Upthrust due to $2cm = 2 \times a^2$ This should be balanced by 200g mass.$\therefore\text{2a}^2=200,\text{a}=10\text{m}^2$
$\pi\text{r}^2=10$
$\text{r}=\sqrt{\frac{10}{\pi}}\text{cm}$
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Question 741 Mark
Is surface tension a vector?
Answer
Surface tension $\Big[\sigma=\frac{\text{W.D.}}{\text{Changr in Surface Area}}\Big]$ so, $\sigma$ is not a vector as it is equal to the work done per unit change in surface area.
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Question 751 Mark
A block of ice is floating in a liquid of specific gravity 1.2 contained in the beaker. What will be the effect on the level of liquid in the beaker when the whole ice melts?
Answer
The level of water in a beaker will rise: It is so because the density of water formed by melting of ice is less than the density of liquid in a beaker. Due to which the volume of the water formed by melting the ice will be more than the volume of the portion of the ice in liquid while floating in liquid.
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Question 761 Mark
What is the acceleration of a body falling through a viscous medium after terminal velocity is reached?
Answer
Zero, because the body after attaining terminal velocity will continue moving with same velocity through the viscous medium.
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Question 771 Mark
Why soap bubble bursts after some time?
Answer
Soap bubble bursts after some time because the pressure inside it become more than the outside pressure.
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Question 781 Mark
The pressure is increased on a gas, then what would be its effect on the viscosity?
Answer
Viscosity of a gas remains unchanged with increased pressure.
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Question 791 Mark
If a capillary tube of insufficient length is dipped into a liquid, what will happen to the liquid rising?
Answer
The liquid will rise to the level available and form a meniscus of large value.
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Question 801 Mark
Why do we prefer mercury in a barometer?
Answer
There are two main reasons of using mercury:
  1. Very high density of mercury.
  2. Negligible vapour pressure of mercury.
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Question 811 Mark
On what factors does the critical speed of fluid flow depend?
Answer
The critical speed of a fluid depends on (a) diameter of tube, (b) density of fluid, (c) coefficient of viscosity of the fluid.
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Question 831 Mark
Explain why When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers.
Answer
By doing so the area of outlet of water jet is reduced, so velocity of water increases according to equation of continuity, Area × Velocity = Constant.
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Question 841 Mark
Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli's equation? Explain.
Answer
No, it does not matter if one uses gauge instead of absolute pressures in applying Bernoulli's equation unless the atmospheric pressure at the two points where, Bernoulli's equation is applied are significantly different.
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Question 851 Mark
Two soap bubbles have radii in the ratio 2 : 3. Calculate the ratio of work done in blowing these bubbles.
Answer
$\text{W}_1=2\times\sigma\times4\pi\text{r}^2_1$$\text{W}_2=2\times\sigma\times4\pi\text{r}^2_2$
$\frac{\text{W}_1}{\text{W}_2}=\Big(\frac{\text{r}_1}{\text{r}_2}\Big)^2=\frac49$
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Question 861 Mark
If the torricellian tube is tilted by 30° with the vertical how much length of mercury will stand at atmospheric pressure at sea-level?
Answer
Mercury rises in the tube is for atmospheric pressure up to 76cm of vertical length. If it is tilted also, the vertical length should be same.
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Question 881 Mark
Two liquids of equal mass and different densities $\rho_1$ and $\rho_2$ are mixed, what is the density of the mixture?
Answer
Valumes of the two liquids are $\frac{\text{m}}{\rho_1}$ and $\frac{\text{m}}{\rho_2}.$$=\frac{2\text{m}}{\frac{\text{m}}{\rho_1}+\frac{\text{m}}{\rho_2}}=\frac{2\rho_1\rho_2}{(\rho_1+\rho_2)}$
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Question 891 Mark
  1. How do trees draw water from the ground?
  2. The radius of a capillary tube is doubled. What change will take place in the height of the capillary rise?
  3. In a capillary tube water descends and not rises. Guess the material of the capillary tube.
Answer
  1. Capillary action.
  2. Capillary rise will be halved as $\text{h}\propto\frac{1}{\text{r}}$
  3. Paraffin wax.
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Question 901 Mark
Explain why Atmospheric pressure at a height of about 6km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100km.
Answer
Density of air is the maximum near the sea level. Density of air decreases with increase in height from the surface. At a height of about 6km, density decreases to nearly half of its value at the sea level. Atmospheric pressure is proportional to density. Hence, at a height of 6km from the surface, it decreases to nearly half of its value at the sea level.
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Question 911 Mark
Why does oil form a thin film over the surface of water?
Answer
Oil has low surface tension than water. So, it forms a thin layer over water.
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Question 921 Mark
Can two streamlines cross each other, why?
Answer
Two streamlines can never cross each other because if they cross them at the point of intersection, there will be two possible direction of flow of fluid which is impossible for streamlines.
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Question 931 Mark
When do we say that a floating body is in stable equilibrium?
Answer
When the upthrust balances the weight of the body, the floating body is in equilibrium.
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Question 941 Mark
How does viscous force differ from normal friction?
Answer
It depends on the area of the layer and velocity gradient in contrast to normal friction.
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Question 951 Mark
How does the rate of flow of a liquid through a tube depend on the radius of its bore?
Answer
Rate of flow of a liquid through a tube is directly proportional to the fourth power of the radius of its bore i.e., $\text{V}\propto\text{r}^4$
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Question 961 Mark
Can Bernoulli's equation be used to describe the flow of water through a rapid in a river? Explain.
Answer
No, Bernoulli's equation cannot be used to describe the flow of water through a rapid in a river because Bernoulli's equation can be utilised only for streamline flow.
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Question 971 Mark
Why, surface tension of all lubricating oils and paint is kept low?
Answer
So, they can spread over large area easily.
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Question 981 Mark
How excess pressure varies with the radius of bubble of drop?
Answer
$\text{P}\propto\frac{1}{\text{r}}.$
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Question 991 Mark
If two row-boats happen to sail parallel, and close of each other, they experience a force which pulls them towards each other. Give reasons for it.
Answer
When the boats come closer to each other, the air velocity between the narrow gap increases and pressure decreases. Thus the boats are further pushed towards each other.
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Question 1001 Mark
What will be the ratio of the velocity of efflux from two holes made with a separation (H - 2h) in a container holding liquid of height 'H' and one hole at a depth ‘h' from its bottom? Give reason.
Answer
1 : 1 as the velocity of efflux will be the same at two places-both at a depth ‘h' from the free surface and at a height 'H' from the bottom.
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Question 1011 Mark
How a raincoat become waterproof?
Answer
If the angle of contact between water and the material of the raincoat is obtuse, then rainy water does not wet the raincoat. Thus, the raincoat becomes waterproof.
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Question 1021 Mark
What is the effect:
  1. Of highly soluble impurities on the surface tension of a liquid?
  2. Of less soluble impurities on the surface tension of a liquid?
  3. On the angle of contact when the temperature of a liquid is increased?
Answer
  1. The surface tension is increased.
  2. The surface tension decreases.
  3. The angle of contact decreases.
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Question 1031 Mark
What is the effect of solute on the surface tension of a liquid?
Answer
If solute is highly soluble-surface tension increases. If solute is less soluble, surface tension decreases.
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Question 1051 Mark
If a wet piece of wood burns, then water droplets appear on the other end, why?
Answer
When a piece of the wood burns, then steam formed and water appear in the form of drops due to surface tension on the other end.
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Question 1061 Mark
A number of small drops of mercury condense isothermally to form a single drop. What will be the effect on temperature of the drop?
Answer
Temperature of the drop remains unchanged.
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Question 1071 Mark
Obtain the dimensional formula for coefficient of viscosity.
Answer
According to Stoke's law, viscous force $\text{F}=6\text{}\pi\eta\text{r}\upsilon$$\therefore$ Demensions of $\eta$ are $\frac{[\text{F}]}{\text{[r]}[\upsilon]}=\frac{\text{[M L T}^{-2}]}{[\text{L}]\times[\text{LT}^{-1}]}[\text{M}^1\text{L}^{-1}\text{T}^{-1}].$
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Question 1081 Mark
How will a mercury barometer's height change, if we introduce some water vapour into it.
Answer
Because water vapour exerts pressure. Thus, the barometric height decreases.
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Question 1091 Mark
In soldering, addition of flux makes soldering easy. Why?
Answer
The addition of flux reduces the surface tension of molten tin, hence it spreads.
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Question 1101 Mark
A hot liquid moves faster than a cold liquid. Why?
Answer
The viscosity of liquid decreases with the increase in temperature. Therefore, viscosity of hot liquid is less than that of cold liquid. Due to this, hot liquid moves faster than the cold liquid.
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Question 1111 Mark
How does the viscosity of gases depend upon temperature?
Answer
For gases, $\eta\propto\text{T}^{\frac12}$
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Question 1121 Mark
Why does a spinning cricket ball in air not follow a parabolic path?
Answer
This is due to Magnus effect.
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Question 1141 Mark
How does the viscous force between two layers of a liquid depend upon the relative velocity between two layers?
Answer
The viscous force between two layers increases with the increase in relative velocity.
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Question 1151 Mark
The diameter of ball A is twice of that of B. What will be the ratio of their terminal velocities in water?
Answer
As terminal velocity $\propto$ $(radius ~of ~ball)^2$ therefore, ratio of terminal velocities of A and B will be 4 : 1.
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Question 1161 Mark
The blood pressure at the feet is more than the blood pressure at the head. Give reason.
Answer
The pressure varies with height of liquid column. So, at a lower level (feet), the pressure is more than at the top (head).
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Question 1171 Mark
What will be the effect on the angle of contact of a liquid if the temperature increases?
Answer
The angle of contact of a liquid increases with the increase in temperature.
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Question 1181 Mark
The terminal velocity of a copper ball of radius $2.0 mm$ falling through a tank of oil at $20^{\circ} C$ is $6.5 \ cm s ^{-1}$. Compute the viscosity of the oil at $20^{\circ} C$. Density of oil is $1.5 \times 10^3 \ kg m ^{-3}$, density of copper is $8.9 \times 10^3 \ kg m ^3$.
Answer
$\text {We have } v_{ t }=6.5 \times 10^{-2} ms ^{-1}, a=2 \times 10^{-3} m ,$
$g=9.8 ms ^{-2}, \rho=8.9 \times 10^3 \ kg m ^{-3},$
$\sigma=1.5 \times 10^3 \ kg m ^{-3} . \text { From Eq. }(9.18)$
$\eta=\frac{2}{9} \times \frac{\left(2 \times 10^{-3}\right)^2 m ^2 \times 9.8 m s ^{-2}}{6.5 \times 10^{-2} m s ^{-1}} \times 7.4 \times 10^3 \ kg m ^{-3}$
$=9.9 \times 10^{-1} \ kg m ^{-1} s ^{-1}$
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Question 1191 Mark
The density of the atmosphere at sea level is $1.29 kg / m ^3$. Assume that it does not change with altitude. Then how high would the atmosphere extend?
Answer
We use Eq. (9.7)
$\rho g h=1.29 \ kg m ^{-3} \times 9.8 m s ^2 \times h m =1.01 \times 10^5 Pa$
$\therefore h=7989 m \approx 8 \ km$
In reality the density of air decreases with height. So does the value of $g$. The atmospheric cover extends with decreasing pressure over $100 \ km$. We should also note that the sea level atmospheric pressure is not always $760 \ mm$ of Hg. A drop in the Hg level by $10 \ mm$ or more is a sign of an approaching storm.
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Question 1201 Mark
What is the pressure on a swimmer 10 m below the surface of a lake?
Answer
Here
$
\begin{aligned}
h & =10 m \text { and } \rho=1000 kg m ^{-3} \text {. Take } g=10 m s ^{-2} \\
& \text { From Eq. }(9.7) \\
P & =P_{ a }+\rho g h \\
& =1.01 \times 10^5 Pa +1000 kg m ^{-3} \times 10 m s ^{-2} \times 10 m \\
& =2.01 \times 10^5 Pa \\
& \approx 2 atm
\end{aligned}
$

This is a $\text{100 %}$ increase in pressure from surface level. At a depth of $\text{1 km}$, the increase in pressure is $\text{100 atm}$ ! Submarines are designed to withstand such enormous pressures.
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Question 1211 Mark
The two thigh bones (femurs), each of cross-sectional area $10 cm ^2$ support the upper part of a human body of mass 40 kg. Estimate the average pressure sustained by the femurs.
Answer
Total cross-sectional area of the femurs is $A=2 \times 10 cm ^2=20 \times 10^{-4} m ^2$. The force acting on them is $F=40 kg wt =400 N$ (taking $g=10 m s ^{-2}$ ). This force is acting vertically down and hence, normally on the femurs. Thus, the average pressure is
$
P_{a v}=\frac{F}{A}=2 \times 10^5 N m ^{-2}
$
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