10.If you double the radius of the capillary tube, what will be the drop in height rise in the tube ? 1

- Why do liquids rise in a capillary tube ? 1

12.What is the impact on surface tension when (i) impurity is increased, and (ii) temperature is 1 decreased ?

13.When two soap bubbles stay in contact, what is the radius of the interface ? 1

14.Two liquids of equal mass and different densities ρ_{1} and ρ_{2} are mixed, what is the density of the 1 mixture ?

15.When 200 g mass placed in a cylindrical beaker of base area ‘a’ is removed, the vertical length 1 comes out of water by 2 cm. What is the radius of the cylinder ?

16.The blood pressure at the feet is more than the blood pressure at the head. Give reason. 1

17.Why do the asbestos roof of houses get lifted in hurricane ? 1

18.How does viscous force differ from normal friction ? 1

19.What is the relation for maximum range of water coming out from an orifice on the side wall of a 1 tank ?

20.What is the excess pressure in a soap bubble of radius 10 mm, if surface tension is 2.5 × 10^{−2 }1 N/m ?

21.The bags and suitcases are provided with broad handles. Why ? 1

22.If a mercury barometer is fitted such that the angle made with the vertical is 30°, what will be the 1 height of mercury column under one atmosphere ?

23.Show the variation of pressure in the atmosphere with height in km. Considering that the density 1 of air is not dependent on pressure.

24.Why is the dome of water reservoir thick at the bottom ? 1

25.A square framed with a wire of side ‘L’ is dipped in a liquid. On taking out, a membrane is 1 formed. What will be the force acting on the frame if the surface tension of liquid is S ?

26.Why does a soft plastic bag weigh the same when empty as when filled with air at atmospheric 1 pressure ?

27.Why do we prefer mercury in a barometer ? 1

28.If we use water instead of mercury in a barometer, what will be the height of water ? 1

29.A number of small drops of mercury condense isothermally to form a single drop. What will be 1 the effect on temperature of the drop ?

30.What is the work done in blowing a soap bubble of radius ‘r’ and surface tension ‘σ’ ? 1

31.What will be the effect on the angle of contact of a liquid if the temperature increases ? 1

32.When a shaving brush is taken out of water its hairs cling together. Why ? 1

33.Surface tension of all lubricating oils and paints is kept low. Why ? 1

34.In soldering, addition of flux makes soldering easy. Why ? 1

35.Why does the liquid level stay higher below the point B ? 1

36.Why does the cotton wick in an oil filled lamp keep on burning ? 1

37.If two row-boats happen to sail parallel, and close of each other, they experience a force which 1 pulls them towards each other. Give reasons for it.

38.What is the net force acting on the molecule of water, when it is fully inside the water ? 1

39.What is the acceleration of a body falling through a viscous medium after terminal velocity is 1 reached ?

40.How does the viscosity of gases depend upon temperature ? 1

41.Two soap bubbles have radii in the ratio 2 : 3. Calculate the ratio of work done in blowing these 1 bubbles.

42.What is effect on the equilibrium of a physical balance when air is blown below one pan ? 1

43.The diameter of ball A is twice of that of B. What will be the ratio of their terminal velocities in 1 water ?

44.Why water cannot be poured into a bottle with a narrow neck with the aid of glass tube ? 1

45.Water flows faster than honey. Why ? 1

46.Can two streamlines cross each other in a flowing liquid ? 1

47.Why does a small mercury drop assume a spherical shape ? 1

48.Why is it that the smaller bubbles have a greater excess pressure ? 1

49.Why does oil form a thin film over the surface of water ? 1

50.Explain why 1

- The blood pressure in human beings is greater at the feet than at the brain.
- Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sealevel, though the height of the atmosphere is more than 100 km.
- Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

51.Fill in the blanks using the word(s) from list appended with each statement. 1

- Surface tension of liquids generally … with temperatures. (increases/decreases)
- Viscosity of gases … with temperature, whereas viscosity of liquids … with temperature.

(increases/decreases)

- For solids with elastic modulus of rigidity, the shearing force is proportional to …., while for fluidsit is proportional to … . (shear strain/rate of shear strain)
- For a fluid in a steady flow, the increase in flow speed at a constriction follows …… while thedecrease of pressure there follows …… . (conservation of mass/Bernoulli’s principle)
- For the model of a plane in a wind tunnel, turbulence occurs at a … speed for turbulence for anactual plane. (greater/smaller)

52.Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river ? 1 Explain.

53.Does it matter if in one uses gauge instead of absolute pressures in applying Bernoulli’s equation 1 ? Explain.

54.What is the cause far velocity gradient as a liquid flows in a tube of radius ‘r’ with its velocity 1 along the axis being ‘v’ ?

55.Why the speed of a whirl wind in a tornado is alarmingly high ? 1

56.Does Archimedes’ principle hold in a vessel in free fall or in a satellite moving in a circular orbit ? 1

57.Write two factors affecting viscosity. Which one is more viscous : pure water or saline water ? 2

58.A liquid has a definite volume but no shape of its own. Explain. 2

59.When a body is fully or partly immersed in a liquid, name the forces acting on the body. 2

60.What are the conditions for equilibrium of floating bodies ? 2

61.According to Stoke, the viscous force experienced by a sphere of radius r depends on the 2 terminal velocity and viscosity of the liquid besides radius. Derive the formula.

62.A cylindrical jar of cross-sectional area 0.01 m^{2} is filled with water to a height of 50 cm (given 2 figure). It carries a tight fitting piston of negligible mass. Calculate the pressure at the bottom of the jar when a mass of 5 kg is placed on the piston.

63.Calculate the work done in blowing a soap bubble from a radius of 2 cm to 3 cm. The surface 2 tension of the soap solution is 30 dynes cm^{–1}.

64.Derive an expression for the excess of pressure inside an air bubble. 2

65.Two liquids of specific gravity 1.2 and 0.84 are poured into the limbs of a U-tube until the 2 difference in levels of their upper surfaces is 9 cm. What will be the heights of their respective

surfaces above the common surface in U-tube ? What is the pressure at the common surface ? [g =

10 ms^{−2}]

66.When air is blown in between two balls suspended close to each other, they are attracted 2

towards each other. Give reason.

67.As soon as parachute of a falling soldier opens, his acceleration decreases and soon becomes 2

zero. Explain.

68.Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, 2

what will be the new steady velocity ?

69.Oil spreads over the surface of water, whereas, water does not spread over the surface of oil. 2

Why ?

70.Explain why “A drop of liquid under no external force is always spherical in shape”. 2

71.What is the significance of : (i) wetting agents used by dyers, and (ii) water proofing agents ? 2

72.The antiseptics used for cuts and wounds in the human flesh have low surface tensions. Why ? 2

73.It is advised not to stand near a running train. Why ? 2

74.A hydraulic automobile lift is designed to lift cars with maximum mass of 300 kg. The area of 2

cross-section of the piston carrying the load is 425 cm^{2}. What maximum pressure would the smaller piston have to bear ?

75.What height of water column produces the same pressure as a 760 mm high column of mercury 2 ?

76.The excess pressure inside a soap bubble is thrice the excess pressure inside a moving soap 2 bubble. What is the ratio between the volume of the first and second bubble ?

77.Pressure of a gas in a closed cylinder is expressed in the following way : 2

P = P_{a} + hρg,

Identify the expressions for :

(a) Absolute pressure of the gas. (b) Gauge pressure of the gas.

78.Explain why : 2

(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute. (b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.) (c) Surface tension of a liquid is independent of the area of the surface.

(d) Water with detergent dissolved in it should have small angles of contact. (e) A drop of liquid under no external forces is always spherical in shape.

79.Two vessels have the same base area but different shapes. The first vessel takes twice the 2 volume of water than the second vessel requires to fill upto a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases ? If so, why do the vessels filled with water to that same height give different readings on a weighing scale ?

80.Figures (a) shows a thin liquid film supporting a small weight = 4.5 × 10^{–2} N. What is the weight 2 supported by a film of the same liquid at the same temperature in Fig. (b) and (c) ? Explain your answer physically.

81.Water flows through a horizontal pipe of radius 1 cm at a speed of 2 ms^{–1}, what should be the diameter of its nozzle if the water is to come out at a speed of 10 ms^{–1} ?

82.An ice floats in water with about ninetenths of its volume submerged. What is the fractional 3 volume submerged for an iceberg floating on a freshwater lake of a (hypothetical) planet whose gravity is ten times that of the earth ?

83.Two capillaries of same length and radius in the ratio of 1 : 2 are connected in series and a liquid 3 flows through this system under streamline conditions. If the pressure across the two extreme ends of combination is 1 m of water, what is the pressure difference across the (i) first capillary, and (ii) second capillary ?

84.Two vessels of the same size are at the same temperature. One of them holds 1 kg of H_{2} gas 3 and the other holds 1 kg of N_{2} gas.

- Which of the vessels contains more molecules ?
- Which of the vessels is under greater pressure and why ?
- In which vessel is the average molecular speed greater ? How many times greater?

85.Prove that the pressure at a depth h from the free surface of a liquid (P) in a container is P = P_{0 }3 + hρg, where P_{0} is the atmospheric pressure.

86.A boat is floating in a small pond and it carries a large number of big sized stones. If stones are 3 unloaded into water in the pond, will there be an observable change in level of water in the pond ?

87.Establish a relation for the excess pressure on a drop of liquid of surface tension σ, giving 3 reason for its presence.

88.State Pascal’s law. Explain the working of hydraulic lift. 3

89.A cube of wood floating in water supports a 200 g mass resting at the centre of its top face. 3 When the mass is removed, the cube rises 2 cm. Find the volume of the cube.

90.A manometer reads the pressure of a gas in an enclosure as shown in Fig. (a). When a pump 3 removes some of the gas, the manometer reads as in Fig. (b). The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.

- Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in unitsof cm of mercury.
- How would the levels change in case (b) if 13.6 cm of water (immiscible with mercury) arepoured into the right limb of the manometer ? (Ignore the small change in the volume of the gas).

91.A U-tube contains water and methylated spirit separated by mercury. The mercury columns in 4

the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit ?

92.Water flows through a horizontal pipe of which the cross-section is not constant. The pressure is 3

1 cm of mercury where the velocity is 0.35 m/s. Find the pressure at a point where the velocity is 0.65 m/s.

93.Two soap bubbles of different diameters are in contact with a certain portion common to both the 3 bubbles. What will be the shape of the common boundary as seen from inside the smaller bubble ?

Support your answer with a neat diagram. Give reason for your answer.

94.A big size balloon of mass M is held stationary in air with the help of a small block of mass M/2 tied to it by a light string such that both float in mid air. Describe the motion of the balloon and the block when the string is cut. Support your answer with calculations.

95.A liquid drop of diameter 4 mm breaks into 1000 droplets of equal size. Calculate the resultant 3

change in surface energy, the surface tension of the liquid is 0.07 Nm^{–1}.

96.State and prove Bernoulli’s theorem. 5

97.What is viscosity ? What are the factors affecting viscous force in a liquid flowing in a tube ? 5

Derive the relation for the velocity upto which the liquid can have streamlined flow.

98.Define surface tension and surface energy. Write units and dimensions of surface tension. Also 5

prove that surface energy numerically equal to the surface tension.

99.When a drop of mercury (radius R) is split into n similar drops, what is the change in surface 5

energy ?

[σ-surface tension of mercury]

100.State Bernoulli’s theorem. Using it how can you explain the functioning of a venturimeter to find 5

velocity of flow of liquid through a tube ?

101.Define coefficient of viscosity and give its SI unit. On what factors does the terminal velocity of a 5

spherical ball falling through a viscous liquid depend ? Derive the formula :

where the symbols have their usual meaning.

102.(a) Define streamline. 5

- Write any two properties of streamlines.
- Draw streamlines for a clockwise spinning sphere.
- Derive equation of continuity.

103.Explain why 5

- To keep a piece of paper horizontal, you should blow over, not under, it.
- When we try to close a water tap with our fingers, fast jets of water gush through the openingsbetween our fingers.
- The size of the needle of a syringe controls flow rate better than the thumb pressure exerted bya doctor while administering an injection.
- A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel. (e) A spinning cricket ball in air does not follow a parabolic trajectory.

104.(a) State and prove Archimedes’ principle. 5

(b) What would be pressure inside a small air bubble of 0.1 mm radius situated just below the surface of water ? Surface tension of water 72 × 10^{–3} N/m and atmospheric pressure is 1.1 × 10^{5 }N/m^{2}.

105.Prove that velocity of efflux of an ideal liquid through an orifice is equal to the velocity attained 5 by a freely falling body from the surface of the liquid to the orifice. Also find the horizontal range in terms of height. When is this range maximum ?

106.(i) What is the phenomenon of capillarity ? Derive an expression for the rise of liquid in a 5 capillary tube.

(ii) What will happen if the length of the capillary tube is smaller than the height to which the liquid rises ? Explain briefly.

107.A cylindrical vessel of uniform crosssection contains liquid upto a height ‘H’. At a depth ‘h’ = H/2 5 below the free surface of the liquid there is an orifice. Using Bernoulli’s theorem, find the velocity of efflux of liquid.

108.What is the density of ocean water at a depth where the pressure is 80.0 atm, given that its 4 density at the surface is 1.03 × 10^{3} kg m^{−3} ?

Compressibility of water = 45.8 × 10^{−11} Pa^{−1}.

Given : 1 atmosphere = 1.013 × 10^{5} Pa.

109.The figure adjoining shows a hydraulic press with the larger piston of diameter 35 cm at a height of 1.5 m relative to the smaller piston of diameter 10 cm. The mass on the smaller piston is 20 kg. What is the force exerted on the load by the larger piston ? The density of oil in the press is 750 kg m−3.

110.A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between 4 the wire and the light slider supports a weight of 1.5 × 10^{−2} N (including the weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film ?

111.A 20 N metal block is suspended by a spring balance and beaker containing some water is 4 placed on the weighing machine which reads 36 N. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now reads 16 N. What will be reading of the weighing machine ?

112.Water rises to a height of 10 cm in a certain capillary tube. The level of mercury in the same 4 tube is depressed by 3.42 cm. Compare the surface tensions of water and mercury. Specific gravity of mercury is 13.6 g/cc and angle of contact for water and mercury are zero and 135° respectively.

113.A fully loaded Boeing aircraft has a mass of 3.3 × 10^{5} kg. Its total wing area is 500 m^{2}. It is in 4 level flight with a speed of 960 km/h.

- Estimate the pressure difference between the lower and upper surfaces of the wings.
- Estimate the fractional increase in the speed of the air on the upper surface of the wing relativeto the lower surface. [Density of air = 1.2 kg m
^{–3}].

114.The manual of a car instructs the owner to inflate the tyres to a pressure of 200 kPa : 4

- What is the recommended gauge pressure ?
- What is the recommended absolute pressure ?
- If, after the required inflation of the tyres, the car is driven to a mountain peak, where the

atmospheric pressure is 10% below that at sea level. What will the tire gauge read ?

115.The area of cross-section of wider tube is 800 cm^{2} in the figure. If a mass of 16 kg is placed as 4

the massless piston, find the difference in the level of water in the two tubes.

116.A tank 5 m high is half–filled with water and then filled to the top with oil of density 0.85 g/cc. 4

What is the pressure at the bottom of the tank due to these liquids ?

117.A solid floats with 1/4th of its volume above the surface of water. Calculate the density of the 4

solid.

118.A glass plate of length 10 cm, breadth 4 cm and thickness 0.4 cm weighs 20 g in air. It is held 4

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.

119.What is the pressure inside a drop of mercury of radius 3.0 mm at room temperature ? Surface 4 tension of mercury at that temperature (20°C) is 4.65 × 10^{−1} Nm^{−1}. The atmospheric pressure is 1.01 × 10^{5} Pa. Also give the excess pressure inside the drop.

120.If a number of little droplets of water of surface tension S, all of the same radius r combine to 4 form a single drop of radius R and the energy released is converted into K.E. Find the velocity acquired by the bigger drop. If the energy released is converted into heat, find the rise in temperature.

121.A 16 cm^{3} volume of water flows per second through a capillary tube of radius r cm and of length 4 l cm when connected to a pressure head of h cm of water. If a tube of the same length and radius r/2 is connected to the same pressure head, find the mass of water flowing per minute through the tube.

122.What should be the average velocity of water in a tube of diameter 2.0 cm so that the flow is 4 laminar ? The viscosity of water is 0.001 N m^{−2} s.

123.A plane is in level flight at constant speed and each of its two wings has an area of 25 m^{2}. If the 4 speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg m^{–3}).

124.A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of 4 cross-section of the piston carrying the load is 425 cm^{2}. What maximum pressure would the smaller piston have to bear ?

125.A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a 4 diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor ?

126.Torricelli’s barometer used mercury. Pascal duplicated it using French wine of density 984 kmm^{– }4 ^{3}. Determine the height of the wine column for normal atmospheric pressure.

127.Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the 4 amount of glycerine collected per second at one end is 4.0 × 10^{–3} kg s^{–1}, what is the pressure difference between the two ends of the tube ? (Density of glycerine = 1.3 × 10^{3} km m^{–3} and viscosity of glycerine = 0.83 Pa). [You may also like to check if the assumption of laminar flow in the tube is correct]

128.In a test experiment on a model aeroplane in a wind tunnel, the flow speeds of the upper and 4 lower surfaces of the wing are 70 m s^{–1} and 63 m s^{–1 }respectively. What is the lift on the wing if its area is 2.5 m^{2} ? (Take the density of air to be 1.3 kg m^{–3}).

129.The cylindrical tube of a spray pump has a cross-section of 8.0 cm^{2} one end of which has 40 4 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^{–1}, what is the speed of the ejection of the liquid through the holes ?

130.Figures (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is 4 incorrect ? Why ?

131.A tank with a square base of area 1.0 m^{2} is divided by a vertical partition in the middle. The 4 bottom of the partition has a small-hinged door of area 20 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.

132.In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 4

× 10^{–5} m and density 1.2 × 10^{3} kg m^{–3} ? Take the viscosity of air at the temperature of the experiment to be 1.8 × 10^{–5} Pa s. How much is the viscous force on the drop at that speed ?

Neglect buoyancy of the drop due to air.

133.Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open 4 at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube ? Surface tension of water at the temperature of the experiment is 7.3 × 10^{–2 }Nm^{–1}. Take the angle of contact to be zero and density of water to be 1.0 × 10^{3} kg m^{–3} (g = 9.8 m s^{–2}).

134.During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000 Pa. 4 At what height must the blood container be placed so that blood may just enter the vein ? [Use the density of whole blood as 1.06 × 10^{3} kg m^{–3}].

135.(a) What is the largest average velocity of blood flow in an artery of radius 2 × 10^{–3} m if the flow 4

must remain laminar ? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084

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