Mechanical Properties of Fluids is a conceptual and scoring chapter in Class 11 Physics that explains the behavior of liquids and gases at rest and in motion. This chapter covers key topics such as pressure in fluids, Pascal’s law, buoyancy, Archimedes’ principle, surface tension, viscosity, Bernoulli’s theorem, and fluid flow, which are important for school exams and competitive exams like JEE and NEET.
NCERT Solutions for Class 11 Physics Chapter 9 – Mechanical Properties of Fluids are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear derivations, diagrams, and solved numericals, helping students understand fluid mechanics concepts clearly and score well in Class 11 examinations.
NCERT Solutions for Class 11 Physics Chapter 9 – Mechanical Properties of Fluids
Q.
Explain why
(a) The blood pressure in humans is greater at the feet than at the brain
(b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km
(c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.
Q.
Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain.
Q.
A manometer reads the pressure of a gas in an enclosure as shown in Fig. 10.25 (a) When a pump removes some of the gas, the manometer reads as in Fig. 10.25 (b)
The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.
(a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury.
(b) How would the levels change in case (b) if 13.6 cm of water (immiscible with mercury) are poured into the right limb of the manometer? (Ignore the small change in the volume of the gas).
Q.
What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20°C) is 2.50 ×10–2 N m–1? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is 1.01 × 105 Pa).
Q.
A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?
Q.
The cylindrical tube of a spray pump has a cross-section of 8.0 cm2 one end of which has 40 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 ejection of the liquid through the holes?
Q.
Figures 10.23 (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect? Why?
Q.
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and 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 m2? Take the density of air to be 1.3 kg m–3.
Q.
Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the 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 × 103 kg m–3 and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of lamina r flow in the tube is correct].
Q.
Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river? Explain.
Q.
Explain why
(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
Q.
In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)
Q.
A U-tube contains water and methylated spirit separated by mercury. The mercury columns in 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?
Q.
A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm2. What maximum pressure would the smaller piston have to bear?
Q.
A vertical off-shore structure is built to withstand a maximum stress of 109 Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.
Q.
Torricelli’s barometer used mercury. Pascal duplicated it using French wine of density 984 kg m–3. Determine the height of the wine column for normal atmospheric pressure.
Q.
A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor?
Q.
Explain why
(a) To keep a piece of paper horizontal, you should blow over, not under, it
(b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
(c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
(d) 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
Q.
Fill in the blanks using the word(s) from the list appended with each statement:
(a) Surface tension of liquids generally . .. with temperatures (increases /decreases)
(b) Viscosity of gases . . . with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
(c) 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)
(d) For a fluid in a steady flow, the increase in flow speed at a constriction follows
(conservation of mass / Bernoulli’s principle)
(e) For the model of a plane in a wind tunnel, turbulence occurs at a . . . speed for turbulence for an actual plane (greater / smaller)
Q.
(a) It is known that density ρ of air decreases with height y as
ρ = ρ0e-y/y0
Where ρ0 =1.25 kg m–3 is the density at sea level, and y0 is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of g remains constant.
(b) A large He balloon of volume 1425 m3 is used to lift a payload of 400 kg. Assume that the balloon maintains constant radius as it rises. How high does it rise?
[Take y0 = 8000 m and ρHe= 0.18 kgm–3].
NCERT Solutions for Class 11 Physics Chapter 9 – Mechanical Properties of Fluids
Q.1) Explain why:
(a) The blood pressure in humans is greater at the feet than at the brain.
Answer:
The pressure of a liquid is given by the relation
P=hρg
where ρ is the density of the liquid and h is the height of the liquid column.
From this relation, it is clear that pressure is directly proportional to height. Since the feet are at a greater vertical distance below the heart compared to the brain, the height of the blood column is greater at the feet. Therefore, the blood pressure at the feet is higher than at the brain.
(b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at sea level, although the height of the atmosphere is more than 100 km.
Answer:
The density of air is maximum near sea level and decreases rapidly with increase in height. Most of the atmospheric air is concentrated in the lower layers of the atmosphere.
At a height of about 6 km, the air density becomes nearly half of its value at sea level. Hence, the atmospheric pressure at this height also reduces to nearly half, even though the atmosphere extends beyond 100 km.
(c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.
Answer:
When pressure is applied to a liquid, it is transmitted equally in all directions. Hydrostatic pressure does not have any specific direction associated with it.
Since pressure at a point acts equally in all directions, it has only magnitude and no direction. Therefore, hydrostatic pressure is a scalar quantity.
Q.2) Fill in the blanks:
| Statement |
Correct Answer |
| (a) Surface tension of liquids generally ______ with temperature. |
Decreases |
| (b) Viscosity of gases ______ with temperature, whereas viscosity of liquids ______ with temperature. |
Increases; Decreases |
| (c) 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 |
| (d) For a fluid in steady flow, the increase in flow speed at a constriction follows ______. |
Conservation of mass (and Bernoulli’s principle) |
| (e) For the model of a plane in a wind tunnel, turbulence occurs at a ______ speed compared to the actual plane. |
Greater |
Q.3) Numerical Problem: Off-shore Structure Suitability
Question:
A vertical off-shore structure is designed to withstand a maximum stress of 109 Pa. Is it suitable for an oil well in the ocean at a depth of 3 km?
Solution:
Maximum stress the structure can withstand
=109Pa
Depth of ocean
d=3×103m
Density of seawater
ρ=103kg m−3
Acceleration due to gravity
g=9.8m s−2
Hydrostatic pressure:
P=ρdg P=103×3×103×9.8 P=2.94×107Pa
Conclusion:
Since the pressure exerted by the ocean water (2.94×107 Pa) is much less than the maximum stress the structure can withstand (109 Pa), the structure is suitable for the oil well.
Q.4) Can Bernoulli’s equation be used for a rapid in a river?
Answer:
No. Bernoulli’s equation is applicable only for streamline (laminar) flow. River rapids involve turbulent flow, so Bernoulli’s equation cannot be applied.
Q.5) Does it matter if one uses gauge pressure instead of absolute pressure in Bernoulli’s equation?
Answer:
No, it does not matter. When Bernoulli’s equation is applied between two points, the atmospheric pressure term cancels out. Hence, either gauge pressure or absolute pressure can be used.
Q.6) Figure Analysis: Venturimeter Flow
Answer:
According to the equation of continuity (Av=constant), when the cross-sectional area of the pipe decreases, the speed of the fluid increases.
By Bernoulli’s principle, an increase in speed leads to a decrease in pressure. Since the height of the liquid column in the pipe is directly related to pressure, the water level in pipe 2 should be lower.
Therefore, figure (b) is correct, and figure (a) is incorrect.
FAQs: Class 11 Physics Chapter 9 – Mechanical Properties of Fluids
Q1. Is Mechanical Properties of Fluids important for exams?
Yes, it is a high-weightage chapter in mechanics for Class 11.
Q2. Which topics are most important in this chapter?
Pascal’s law, Archimedes’ principle, Bernoulli’s theorem, surface tension, and viscosity.
Q3. Are numericals asked from this chapter?
Yes, pressure, buoyancy, and Bernoulli-based numericals are very common.
Q4. Are derivations important here?
Yes, derivations related to Bernoulli’s theorem and excess pressure formulas are frequently asked.
Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved numericals and diagrams.