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**Exercise : ** Solutions of Questions on Page Number : **268**

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Q1 :
**
**

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.

**Answer :**

**(a)** The pressure of a liquid is given by the relation:

*P* = *hÃÂ*g

Where,

*P* = Pressure

*h* = Height of the liquid column

*ÃÂ* = Density of the liquid

g = Acceleration due to the gravity

It can be inferred that pressure is directly proportional to height. Hence, the blood pressure in human vessels depends on the height of the blood column in the body. The height of the blood column is more at the feet than it is at the brain. Hence, the blood pressure at the feet is more than it is at the brain.

**(b)** 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 6 km, density decreases to nearly
half of its value at the sea level. Atmospheric pressure is
proportional to density. Hence, at a height of 6 km from the
surface, it decreases to nearly half of its value at the sea
level.

**(c)** When force is applied on a liquid, the pressure in the
liquid is transmitted in all directions. Hence, hydrostatic
pressure does not have a fixed direction and it is a scalar
physical quantity.

Answer needs Correction? Click Here

Q2 :
**
**

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

**Answer :**

**(a)** The angle between the tangent to the liquid surface at
the point of contact and the surface inside the liquid is called
the angle of contact (*θ*), as shown
in the given figure.

*S*_{la}, *S*_{sa}, and
*S*_{sl} are the respective interfacial tensions
between the liquid-air, solid-air, and solid-liquid interfaces.
At the line of contact, the surface forces between the three
media must be in equilibrium, i.e.,

The angle of contact *θ* , is obtuse
if *S*_{sa} *< S*_{la} (as in the
case of mercury on glass). This angle is acute if
*S*_{sl}*< S*_{la} (as in the case
of water on glass).

**(b)** Mercury molecules (which make an obtuse angle with
glass) have a strong force of attraction between themselves and a
weak force of attraction toward solids. Hence, they tend to form
drops.

On the other hand, water molecules make acute angles with glass. They have a weak force of attraction between themselves and a strong force of attraction toward solids. Hence, they tend to spread out.

**(c)** Surface tension is the force acting per unit length at
the interface between the plane of a liquid and any other
surface. This force is independent of the area of the liquid
surface. Hence, surface tension is also independent of the area
of the liquid surface.

**(d)** Water with detergent dissolved in it has small angles
of contact (*θ*). This is because for
a small *θ*, there is a fast
capillary rise of the detergent in the cloth. The capillary rise
of a liquid is directly proportional to the cosine of the angle
of contact (*θ*). If
*θ* is small, then
cos*θ* will be large and the rise of
the detergent water in the cloth will be fast.

**(e)** A liquid tends to acquire the minimum surface area
because of the presence of surface tension. The surface area of a
sphere is the minimum for a given volume. Hence, under no
external forces, liquid drops always take spherical shape.

Answer needs Correction? Click Here

Q3 :
**
**

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)

**Answer :**

Q4 :
**
**

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

**Answer :**

Q5 :
**
**

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?

**Answer :**

Q6 :
**
**

Toricelli'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.

**Answer :**

Q7 :
**
**

A vertical off-shore structure is built to withstand a maximum
stress of 10^{9} 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.

**Answer :**

Q8 :
**
**

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 cm^{2}. What maximum pressure
would the smaller piston have to bear?

**Answer :**

Q9 :
**
**

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?

**Answer :**

Q10 :
**
**

In problem 10.9, 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)

**Answer :**

Q11 :
**
**

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

**Answer :**

Q12 :
**
**

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

**Answer :**

Q13 :
**
**

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 x
10^{-3} kg
s^{-1}, what is the pressure
difference between the two ends of the tube? (Density of
glycerine = 1.3 x
10^{3} kg m^{-3} and
viscosity of glycerine = 0.83 Pa s). [You may also like to check
if the assumption of laminar flow in the tube is correct].

**Answer :**

Q14 :
**
**

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 m^{2}? Take the density of
air to be 1.3 kg m^{-3}.

**Answer :**

Q15 :
**
**

Figures 10.23 (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect? Why?

**Answer :**

Q16 :
**
**

The cylindrical tube of a spray pump has a cross-section of 8.0
cm^{2} 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?

**Answer :**

Q17 :
**
**

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 x
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?

**Answer :**

Q18 :
**
**

Figure 10.24 (a) shows a thin liquid film supporting a small
weight = 4.5 x
10^{-2} N. What is the weight
supported by a film of the same liquid at the same temperature in
Fig. (b) and (c)? Explain your answer physically.

**Answer :**

Q19 :
**
**

What is the pressure inside the drop of mercury of radius 3.00 mm
at room temperature? Surface tension of mercury at that
temperature (20°C) is 4.65
x
10^{-1} N
m^{-1}. The atmospheric pressure is
1.01 x 10^{5} Pa. Also
give the excess pressure inside the drop.

**Answer :**

Q20 :
**
**

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
x
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 x 10^{5} Pa).

**Answer :**

Q21 :
**
**

A tank with a square base of area 1.0 m^{2} is divided by
a vertical partition in the middle. The 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.

**Answer :**

Q22 :
**
**

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).

**Answer :**

Q23 :
**
**

Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that 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?

**Answer :**

Q24 :
**
**

During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000 Pa. 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 :**

Q25 :
**
**

In deriving
Bernoulli's
equation, we equated the work done on the fluid in the tube to
its change in the potential and kinetic energy. (a) What is the
largest average velocity of blood flow in an artery of diameter 2
x
10^{-3} m if the flow must remain
laminar? (b) Do the dissipative forces become more important as
the fluid velocity increases? Discuss qualitatively.

**Answer :**

Q26 :
**
**

(a) What is the largest average velocity of blood flow in an
artery of radius 2 x
10^{-3} m if the flow must remain
laminar? (b) What is the corresponding flow rate? (Take viscosity
of blood to be 2.084 x
10^{-3} Pa s).

**Answer :**

Q27 :
**
**

A plane is in level flight at constant speed and each of its two
wings has an area of 25 m^{2}. If the 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}).

**Answer :**

Q28 :
**
**

In Millikan's
oil drop experiment, what is the terminal speed of an uncharged
drop of radius 2.0 x
10^{-5} m and density 1.2
x 10^{3} kg
m^{-3}? Take the viscosity of air at
the temperature of the experiment to be 1.8
x
10^{-5} Pa s. How much is the viscous
force on the drop at that speed? Neglect buoyancy of the drop due
to air.

**Answer :**

Q29 :
**
**

Mercury has an angle of contact equal to
140° with soda lime glass. A narrow
tube of radius 1.00 mm made of this glass is dipped in a trough
containing mercury. By what amount does the mercury dip down in
the tube relative to the liquid surface outside? Surface tension
of mercury at the temperature of the experiment is 0.465 N
m^{-1}. Density of mercury = 13.6
x 10^{3} kg
m^{-3}.

**Answer :**

Q30 :
**
**

Two narrow bores of diameters 3.0 mm and 6.0 mm are
joined together to form a U-tube open 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 x
10

**Answer :**

Q31 :
**
**

(a) It is known that density *ÃÂ* of air decreases
with height *y* as

Where *=* 1.25 kg
m^{â€“3} is the density at sea level,
and *y*_{0} 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 gremains constant.

(b) A large He balloon of volume 1425 m^{3} 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 *y*_{0}= 8000 m and = 0.18 kg
m^{â€“3}].

**Answer :**

Physics Part-2 - Physics : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Mechanical Properties Of Fluids ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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