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Q1. If mustard oil and water are dropped out from a tube separately, the mustard oil comes out later than water. Why?

Solution

If mustard oil and water are dropped out from a tube separately, the mustard oil comes out later than water because the coefficient of viscosity of mustard oil is very large as compared to the coefficient of viscosity of water. Hence, water rushes out quickly than mustard oil.

Q2. What is the weight of the body, when it falls with terminal velocity through a viscous medium?

Solution

When a body falling through a viscous medium attains terminal velocity, the apparent weight of the body is balanced by the viscous force due to the medium. Therefore, the weight of a body falling with terminal velocity is zero.

Q3. Bernoulli's theorem is a consequence of which principle?

Solution

Bernoulli's theorem is a consequence of the principle of conservation of energy applied to fluids in a motion.

Q4. A plane is in level flight at constant speed. If the speed of blowing air over the lower wing is 150 km/h and that over the upper wing is 210 km/h, determine the net upward force exerted on the plane. Given area of each wing 20 m². (Take air density to be 1 kg/m³)

Solution

v₁ = 150 km/h = 125/3 m/s v₂ = 210 km/h = 175/3 m/s A = 2 x 20 = 40 m² According to Bernoulli's theorem, we have P₁ - P₂ = 1/2 ρ(v₂² - v₁²)           = 1/2 x 1 [(175/3)² - (125/3)²] = 1/2 [(30625-15625)/9]           = 15000/18 Pa Upward force = (P₁-P₂) x A                    = (15000x40)/18 = 33333.33 N

Q5. State the factors on which the angle of contact depends.

Solution

The angle of contact depends on: a.     The nature of liquid and solid in contact. b.     The medium which exists above the free surface of the liquid. However, it is fixed for a given pair of solid and liquid surrounding medium.

Q6. What are the practical applications of Stoke's law?

Solution

Applications of Stoke's law are as follows: 1. Rain drop do not acquire alarmingly high velocity during their free fall. If this does not happen a person moving in rain would get hurt. 2. While jumping from an airplane, parachute helps us to land safely on the earth. 3. It is used to determine the value of charge on an electron. (Millikan’s oil drop method)

Q7. On the basis of Bernoulli's principle, explain the lift of an airplane.

Solution

The cross-section of the wings of an airplane looks like the aerofoil with streamlines around it. When the aerofoil moves against the wind, the orientation of the wing relative to flow direction causes the streamlines to crowd together above the wing more than those below it. The flow speed on top is higher than that below it. There is an upward force resulting in a dynamic lift of the wings and this balances the weight of the plane.

Q8. Why does the speed of a liquid increase, when it passes through a constriction in a pipe?

Solution

The speed of the liquid increases in accordance with equation of continuity, i.e. a₁v₁= a₂v₂. As the area of cross section and velocity are inversely proportional, hence the speed of liquid increases as pipe becomes narrower.

Q9. Why does deep water run slowly?

Solution

As the depth of water in a river or a stream increases, the area of cross-section available to the flow increases. Consequently, velocity decreases in accordance with the equation of continuity. Thus, deep water runs slowly.

Q10. What is Torricelli's law?

Solution

The velocity of efflux of a liquid is equal to the velocity which a body acquires in falling freely from the free liquid surface to the orifice. This is called Torricelli's law.

Q11. What is the function of a barometer?

Solution

Barometer is a device used to measure pressure.

Q12. Explain why is the velocity of water in a river less on the banks and large in the middle?

Solution

Due to large force of adhesion between the water streams and the bank of the river, the velocity of water is quite small near the bank as compared to that in the middle of it.

Q13. When you rotate a liquid, it comes to rest after some time. Why?

Solution

A liquid set in to rotation comes to rest due to internal friction between the layers of the liquid. This internal friction is called viscosity.

Q14. What is an aerofoil?

Solution

Aerofoil is the name given to a solid object shaped in such a way so as to provide an upward vertical force as it moves horizontally through air. This upward force is what enables aeroplanes to fly.

Q15. State Pascal's Law and its applications.

Solution

According to the Pascal's Law, If pressure is applied to the fluids which are confined then the fluid will transmit the same pressure in all directions at the same rate. Applications of Pascal's Law are: (i) Hydraulic brake (ii)Hydraulic press

Q16. State Bernoulli's theorem.

Solution

Bernoulli's theorem states that for the streamline flow of an ideal liquid, the total energy (the sum of the pressure energy, potential energy and kinetic energy) per unit mass remains constant at every cross-section throughout the flow.

Q17. What are the factors on which the pressure in the liquid at rest depends?

Solution

The pressure in the liquid at rest depends on: (i) Depth of liquid (ii) Density of liquid (iii) Acceleration due to gravity

Q18. Why is ploughing of fields essential?

Solution

Ploughing of fields is essential as it breaks the fine capillaries in the soil, thereby saving the loss of excess water which rises in the capillaries and evaporates.

Q19. State Bernoulli's theorem for an ideal liquid flowing through a horizontal tube.

Solution

According to Bernoulli's theorem, P/ρ + gh + ½v² = constant                     ......(1)   For a horizontal tube, the two ends of the tube will be at the same level (there will be no level difference) Therefore h = 0 From equation (1), we get P/ρ + ½v² = constant Thus, Bernoulli's theorem states that in the streamline flow of ideal liquid through horizontal tube, the sum of pressure energy per unit mass and kinetic energy per unit mass remains constant at any cross-section throughout the flow.

Q20. Two stream lines cannot cross each other. Explain Why?

Solution

The tangent at any point on the streamline gives the direction of flow of liquid molecules at that point. If in case, two streamlines cross each other, then it would mean that the liquid molecule can have different velocities along two different directions, which is against the definition of streamline motion. Hence, two streamlines cannot cross each other.

Q21. When we close a part of the opening of water tap with our finger, fast jets of water gush through the opening. Explain Why?

Solution

As we close the water-tap with our finger, the area of cross-section of the opening between the finger and tap boundary decreases quite appreciably. In accordance with the equation of continuity (a₁v₁ = a₂v₂), the velocity of water increases enormously and fast jets of water gush through the opening.

Q22. What would happen to the equilibrium of a physical balance when air is blown below one of the pans?

Solution

When air is blown below one of the pans, there will be an increase in air velocity due to which the pressure decreases, and hence, the pan goes down.

Q23. Air flows horizontally with the speed of 108 Km/h over the plane roof of the house. If the area of the roof is 28 m² and the density of air is 1.3 kg/m³ calculate the upthrust exerted on the roof.

Solution

ρ = 1.3 kg/m³ v₁= 0 (because there is no air below the roof) v₂= 108 Km/h = 30 m/s According to Bernoulli's theorem, we have P₁+ ½ρv₁² = P₂ + ½ρv₂² P₁ - P₂ = ½ρ (v₂² - v₁²) P₁ - P₂ = ½ρ v₂² Up thrust on the roof is F= (P₁-P₂) x A   = ½ ρv₂² x A   = 1/2 x 1.3 x 30 x 30 × 28   = 16380 N

Q24. Why are the roofs of some houses blown off during a wind storm?

Solution

The high wind blowing over the roof creates a low pressure in accordance with Bernoulli's principle. The pressure below the roof is equal to the atmospheric pressure which is now larger than pressure above the roof. This difference of pressure causes an upward thrust and the roof is lifted up. Once the roof is lifted up, it is blown off with the wind along its direction.

Q25. Why do the hairs of a shaving brush cling together when taken out of water?

Solution

When the brush is taken out of water, the hairs cling together due to surface tension. This happens because the free surface of water tries to acquire a minimum surface area.

Q26. How does Bernoulli's principle help in explaining heart attack?

Solution

In persons suffering with advanced heart condition, the artery gets constricted due to the accumulation of plaque on its inner walls.  In order to drive the blood through this constriction a greater activity of the heart is required. The speed of the flow of the blood in this region is raised which lowers the pressure inside, and the artery may collapse due to this external pressure. The heart exerts further pressure to open this artery and forces the blood through. As the blood rushes through the opening, the internal pressure once again drops leading to a repeat collapse. This may result in heart attack.

Q27. Two bodies of equal weight and volume and having the same shape, except that one has an opening at the bottom and the other is sealed, are immersed to the same depth in water. Which body requires more work to be immersed and why?

Solution

More work is required in case of the body having hole at its bottom. As the liquid enters the hole, more work is required in compressing the air. So, less work is required in case of the sealed body.

Q28. When we swim under water, pressure on our body increases as we go deeper, but yet our body is not crushed due to this pressure. Why?

Solution

When we swim under water, our body is not crushed due to increasing pressure as we go deeper because our body tries to compensate for this pressure by creating an internal pressure which balances this external pressure. But, as we go deeper and deeper, there will be a depth at which our body feels uncomfortable resulting in serious injuries.

Q29. What is capillarity? Give some applications of capillarity.

Solution

The rise and fall of liquid in a capillary tube is called capillarity. Some applications of capillarity are: a.     Towels soak water on account of capillarity. b.     Oil rises in the long narrow spaces between the threads of the wick as they act as a capillary.

Q30. Water is flowing with a speed of 4 m/s in a horizontal pipe of non-uniform area of cross-section decreasing from 0.04 m² to 0.01 m² at pressure 40 x 10⁴ Pa. What will be the pressure at narrower end?

Solution

v₁ = 4 m/s, a₁ = 0.04 m², P₁ = 40 x 10⁴ Pa a₂ = 0.01 m², P₂ = ? According to equation of continuity, we have a₁v₁ = a₂v₂ v₂ = a₁v₁ / a₂ = 0.04 x 4/ 0.01 = 16 m/s According to Bernoulli's theorem, we have P₁+ ½ρv₁² = P₂ + ½ρv₂² P₂ = P₁+ ½ρ(v₁² - v₂²) = 40 x 10⁴ + ½ x 10³ (4² - 16²)     = 40 x 10⁴  - ½ x 10³ x 240     = (400 - 120) x 10³     = 280 x 10³ Pa

Q31. Dirty or greasy stains cannot be cleared by washing with water and we need detergents. Why?

Solution

Yes dirty or greasy stains cannot be cleared by washing with water and we need detergents for the same because water cannot find contact with the greasy or oily molecules, and hence, it cannot wet the surface. We use detergents whose molecules are hairpin like in shape. When we dissolve detergents in water the molecules of detergents get attracted to water and when clothes are dipped in such water the hairpin molecules get attached to the grease, and hence, water and greasy dirt interface is formed. Therefore, detergents are used to reduce the surface tension between water and greasy stain. When clothes are rinsed in water the greasy dirt is washed away by running water.  

Q32. What is meant by an ideal fluid?

Solution

An ideal fluid is the one which is non-viscous, incompressible, and its flow is steady and irrotational.

Q33. At what speed will the velocity of a stream of water be equal to 10 cm of Hg?

Solution

Velocity head = 10 cm of Hg v²/2g = 10 x 13.6 cm of water v² = 2 x 9.80 x 10 x 13.6 v = 516.29 m/s

Q34. What is a dynamic lift?

Solution

If is the force that acts on a body, such as airplane wing, a hydrofoil or a spinning ball, by virtue of its motion through a fluid. It is responsible for the curved path of a spinning ball and the lift of an aircraft.

Q35. What is a streamline flow?

Solution

When a liquid flows such that each particle of the liquid passing a given point moves along the same path and has the same velocity as its predecessor, the flow is called streamline flow or steady flow. That is, at any given point the velocity of each passing fluid particle remains constant in time.

Q36. Explain why, the lubricant oils used in our automobiles should be of high viscosity?

Solution

When oil is used as a lubricant in machines, it forms a thin layer over the metallic parts of the machinery. Hence, during normal working of the machinery, the metallic parts do not come in direct contact with each other. Now, for the oil layer to be effective as a lubricant for a long time, the oil should be of high viscosity. 

Q37. What are the limitations of Bernoulli's theorem?

Solution

There are following limitations of Bernoulli's theorem: (i) In Bernoulli's theorem, the velocity of every particle of liquid across any cross-section is considered uniform which is not correct. The velocity of the particles is different in different layers. (ii) The loss of energy when the liquid is in motion is not considered while some kinetic energy is converted into heat and is lost. (iii) The fluids must be incompressible as the elastic energy of the fluid is not taken into account.

Q38. What happens to the pressure of an ideal liquid when it enters a narrow tube?

Solution

When water flowing in a broader pipe enters a narrow pipe, the area of cross-section for the water to flow decreases, and therefore, the velocity of water increases due to which the pressure of an ideal liquid decreases.

Q39. Why are oils of different viscosities used in automobiles in different seasons?

Solution

The viscosity of lubricant oils decreases with rise in temperature. Therefore, the oil that is suitable as lubricant in summer, may not be suitable in winter. So, the oils of different viscosities are used as lubricant in different seasons.  

Q40. For the soldiers working on high altitudes, packed food are generally dropped with the help of a parachute. Why?

Solution

Due to large structure of parachute, it experience a large viscous force, and hence, while descending through air it acquires very small terminal velocity. Due to this low velocity of decent, the packed food lands safely without being scattered or damaged.