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Explain why
(a)
The blood pressure in humans is greater at the feet than at the brain.
(b)
At morphemic pressure at a height of about 6 km decreases to nearly half 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, and force is a vector.
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Explain why
(a) The angle of contact of mercury with
glass is obtuse, while that of water with glass is acute. Explain.
(b) Water on a clean glass surface tends to
spread out while mercury on the same surface tends to from drops.
(c) Surface tension of liquid is
independent of the area of the liquid surface.
(d) Detergents should have small angles of
contact.
(d) A drop of liquid under no external
forces is always spherical in shape.
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Find in the blanks using the words (s) from the test
appended with each statement.
(a)
Surface tension of liquid 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 from While the decrease of pressure there follows from
(conservation of mass / Bernoullis 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).
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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, the fast jest of water gust
through the openings between our fingers.
(c)
A fluid flowing out of a small hole in a vessel, results in a backward thrust
on the vessel.
(d) The size of the needle of a syringe
controls flow better than the thumb pressure exerted by a doctor while
administering an injection.
(e) A spinning cricket ball in air does not
follow a parabolic trajectory.
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A 50 kg girl wearing high heel shoes balances on a single
heel. The heel is circular with a diameter 1 cm. What is the pressure exerted
by the heel on the horizontal floor?
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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.
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A vertical off-shore structure is built to withstand a
maximum stress of \[{{10}^{9}}\,Pa\]. Is the structure suitable for putting
upon top of an oil well in Bombay High? Take the depth of the sea to be roughly
3 km, and ignore ocean currents.
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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 \[425\,c{{m}^{2}}\]. What maximum pressure would smaller piston have to
bear?
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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 relative density of
spirit?
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In Q.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? (Relative density of mercury = 13.6)
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Can Bernoulli equation be used to describe the flow of water
through a rapid in a river? Explain.
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Does it matter if one uses gauge instead of absolute
pressures in applying Bernoulli's equation. Explain.
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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 \[\text{4 }\!\!\times\!\!\text{ 0 }\!\!\times\!\!\text{
1}{{\text{0}}^{\text{-5}}}{{\text{m}}^{\text{2}}}\], what is the pressure
difference between the two ends of the tube? (density of glycerine \[=1.3\times
{{10}^{3}}\,kg{{s}^{-3}}\] and viscosity of glycerine \[{{\text{l}}_{\text{1}}}\text{=4
}\!\!\times\!\!\text{ 7m;}\]).
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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 is \[1.3\,kg\,\,{{m}^{-3}}\].
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Fig.7. 8 (a) and (b) refer to the steady flow of
(non-viscous) liquid. Which of the two figures is incorrect?
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The cylinderical tube of a spray pump has a cross-section of
\[=1\cdot 49\times {{10}^{-4}}m\] one of which has 40 fine holes each of
diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m per minute, what
is the speed of ejection of the liquid through the holes ?
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A U-shaped wire is dipped in a soap solution, and removed. A
thin soap film formed between the wire and a light slider supports a eight of \[1.5\times
{{10}^{-2}}\,N\] (which includes the small weight of the slider). The length of
the slider is 30 cm. What is the surface tension of the film?
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Fig. 9(a) below shows a thin film supporting a small weight
\[\text{Strain=}\frac{\text{stress}}{\text{modulusnofelasticity}}\text{=}\frac{\text{F/A}}{\text{G}}\]
What is the weight supported by a film of the same liquid at the same
temperature in Fig 7(NCT). 9 (b) and (c)? Explain your answer physically.
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What is the pressure inside a drop of mercury of radius 3.0
mm at room temperature? Surface tension of mercury at that temperature (20C)
is \[{{10}^{8}}\times \pi {{r}^{2}}={{10}^{8}}\times \left( 22/7 \right)\times {{\left(
1\cdot 5\times {{10}^{-2}} \right)}^{2}}=7\cdot 07\times {{10}^{4}}N\]. The
atmospheric pressure is \[1.01\times {{10}^{5}}\,Pa\] . Also give the excess
pressure inside the drop.
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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 \[({{20}^{o}}C)\] is \[{{D}^{2}}\alpha 1/Y\] ? If an air bubble of
the same dimensions were formed at a 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 atm. is \[1.01\times {{10}^{5}}\,Pa\] )
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A tank with a square base of area \[F=mg+mr{{\omega
}^{2}}=mg+mr4{{\pi }^{2}}{{v}^{2}}=\] is divided by a vertical partition in the
middle. The bottom of the partition has a small hinged door of area \[=14\cdot
5\times 9\cdot 8+14\cdot 5\times 1\times 4\times {{\left( 22/7
\right)}^{2}}\times {{2}^{2}}\]The tank is filled with water and an acid (of
relative density \[=142\cdot 1+2291\cdot 6=2433\cdot 7N\]) in the other, both
to a height of 4.0 m. Compute the force necessary to keep the door closed.
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A manometer reads the pressure of a gas in an enclosure as
shown in Fig. 7 (NCT) 11 (b) . The liquid used in manometers is mercury and the
atmospheric pressure is 76 cm of mercury.
(i)
Give the absolute and gauge pressure of the gas in the two cases (in units of
cm. of mercury).
(ii)
How would the levels change in case (b) if \[=0\cdot 5\times
{{10}^{-3}}{{m}^{3}}.\]cm of water are poured into the right limb of manometer?
(Ignore the change in volume of the gas).
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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 up to a particular common height Is the force exerted by water
on the base of the vessel the same m the two cases? If so, why do the vessels
filled with water to that same height give different readings on a weighing
scale?
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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? Density of whole blood =\[p=80\cdot
0\times 1\cdot 013\times {{10}^{5}}pa;\]
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In deriving Bernoullis equation, we equated the work done
on the fluid in the tube to its change in the potential and kinetic energy (a)
How dose the pressure change as the fluid moves along the tube if dissipative
forces are present? (b) Do the dissipative forces become more important as the
fluid velocity increases? Discuss qualitatively.
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(a) What is the largest average velocity of blood flow in an
artery of radius \[2\times {{10}^{-3}}\,m\] if the flow must remain laminar?
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A plane is in level flight at constant speed and each of its
wings has an area of \[\frac{\vartriangle V}{V}=\left( 80\cdot 0\times 1\cdot
013\times {{10}^{5}} \right)\times 45\cdot 8\times {{10}^{-11}}\] 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 \[1\,kg/{{m}^{3}}\])
\[g=9.8\,m/{{s}^{2}}\].
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In Millikan's oil drop experiment, what is the terminal
speed of a drop of radius \[=2\cdot 74\times {{10}^{-5}}\] m and density \[7\times
{{10}^{6}}Pa.\]? Take the viscosity of air at the temperature of the
experiment to be \[\text{L=10 cm}=0\cdot \text{10 m; p}=7\times
{{10}^{6}}\text{Pa;}\]. How much is the viscous force on the drop at that
speed? Neglect buoyancy of the drop due to air.
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Mercury has an angle of contact equal to \[{{140}^{o}}\]
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 mercury surface outside? Surface tension of mercury
at the temperature of the experiment is \[B=\frac{pV}{\vartriangle V}\]Density
of mercury\[p=B\frac{\vartriangle V}{V}=\left( 2\cdot 2\times {{10}^{9}}
\right)\]
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Two narrow bores of diameters 3.0 mm and 6.0 mm are joined
together to form a U shaped 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 \[=2\cdot
026\times {{10}^{4}}\] Take the angle contact to be zero, and density of water
to be \[1\cdot 03\times {{10}^{3}}g{{m}^{-3}}?\]
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(a) It is known that density p of air decreases with height
y (in metres) as \[\rho ={{\rho }_{0}}{{e}^{-y/{{y}_{0}}}}\] where \[1-\frac{1\cdot
30\times {{10}^{3}}}{p'}=3\cdot 712\times {{10}^{-3}}\] is the density at see
level, and \[p'=\frac{1\cdot 30\times {{10}^{3}}}{1-3\cdot 712\times
{{10}^{-3}}}=1\cdot 034\times {{10}^{3}}\text{kg }{{\text{m}}^{\text{-3}}}\]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 \[1425\,{{m}^{3}}\] is used to lift a payload of
400 kg. Assume that the balloon (1 g maintains constant radius as it rises. How
high does it rise?
\[atm=1\cdot
013\times {{10}^{5}}pa.\]
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question_answer32)
A tall cylinder is
filled with viscous oil. A round pebble is dropped from the top with zero
initial velocity. From the plot shown in Fig. Indicate the one that represents
the velocity \[(\upsilon )\] of the pebble as a function of time (t).
(a) 
(b) 
(c)
(d) 
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question_answer33)
Which
of the following diagrams (fig.) does not represent a streamline flow?
(a)
(b) 
(c)
(d)
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question_answer34)
Along
a streamline
(a)
the velocity of a fluid particle remains constant.
(b)
the velocity of all fluid particles crossing a given position is constant.
(c)
the velocity of all fluid particles at a given instant is constant.
(d)
the speed of a fluid particle remains constant.
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question_answer35)
An
ideal fluid flows through a pipe of circular cross-section made of two sections
with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes
is
(a)
9 : 4 (b) 3 : 2
(c)
\[\sqrt{3}:\,\sqrt{2}\] (d) \[\sqrt{2}:\,\sqrt{3}\]
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question_answer36)
The
angle of contact at the interface of water glass is \[{{0}^{o}}\],
Ethylalcohol-glass is \[{{0}^{o}}\], Mercury-glass is \[{{140}^{o}}\] and
Methyliodide-glass is \[{{30}^{o}}\]. A glass capillary is put in a through
containing one of these four liquids. It is observed that the meniscus is
convex. The liquid in the through is
(a)
water (b) ethylalocolol
(c)
mercutry (d) methyliodide
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question_answer37)
6. For a
surface molecule
(a)
the net force on it is zero.
(b)
there is a net downward force.
(c)
the potential energy is less than that of a molecule inside.
(d)
the potential energy is more than that of a molecule inside.
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question_answer38)
Pressure
is a scalar quantity because
(a)
it is the ratio of force to area and both force and area are vectors.
(b)
it is die ratio of the magnitude of the force to area.
(c)
it is the ratio of the component of the force normal to the area.
(d)
it does not depend on the size of the area chosen.
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question_answer39)
A
wooden block with a coin placed on it top, floats in water as shown in Fig. The
distance l and h are shown in the figure. After some time the coin falls into
the water. Then
(a) \[l\] decrease (b)
\[h\] decreases.
(c) \[l\] increases (d)
\[h\] increase
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question_answer40)
With
increase in temperature, the viscosity of
(a)
glass decreases (b) liquids increases
(c)
gases increases (d) liquids decreases
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question_answer41)
Streamline
flow is more likely for liquids with
(a)
high density (b) high viscosity
(c)
low density (d) low viscosity
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question_answer42)
Is viscosity a
vectory?
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question_answer43)
Is
surface tension a vector?
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question_answer44)
Iceberg
floats in water with part of it submerged. What is the fraction of the volume
of iceberg submerged if the density of ice is \[{{\rho
}_{i}}\,\,0.917\,\,g\,\,c{{m}^{-3}}\]?
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question_answer45)
A
vessel filled with water is kept on a weighing pan and the scale adjusted to
zero. A block of mass M and density \[\rho \]is suspended by a massless spring of
spring constant K. This block is submerged inside into the water in the vessel.
What is the reading of the scale?
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question_answer46)
A
cubical block of density r is floating on the
surface of water. Out of its height L, fraction \[x\] is submerged in water.
The vessel is in an elevator accelerating upward with acceleration a. What is
the fraction immersed?
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question_answer47)
The
sap in trees, which consists mainly of water in summer, rises in a system of
capillaries of radius \[r=2.5\times {{10}^{5}}m\]. The surface tension of sap
is
\[T=7.28\times {{10}^{-2}}\,N{{m}^{-1}}\] and the angle of contact is \[{{0}^{o}}\].
Does surface tension alone account for the supply of water to the top of all
trees?
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question_answer48)
The
free surface of oil in a tanker, at rest, is horizontal. If the tanker starts
accelerating the free surface will be titled by an angle \[\theta \]. If the
acceleration is \[a\,m\,{{s}^{-2}},\] what will be the slope of the free surface?
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question_answer49)
Two
mercury droplets of radii 0.1 cm and 0.2 cm collapse into one single drop. What
amount of energy is released? The surface tension of mercury \[T=435.5\times
{{10}^{-3}}\,N\,{{m}^{-1}}\].
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question_answer50)
If a drop of liquid
breaks into smaller droplets, it results in lowering of temperature of the
droplets. Let a drop of radius R, break into N small droplets each of radius r.
Estimate
the drop in temperature.
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question_answer51)
The sufrace tension
and vapour pressure of water at \[{{20}^{o}}C\] is \[7.28\times
{{10}^{-2}}\,N\,{{m}^{-1}}\] and \[2.33\times {{10}^{3}}\,Pa\], respectively. What
is the radius of the smallest spherical water droplet which can form without
evaporating at \[{{20}^{o}}C\]?
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question_answer52)
(a)
Pressure decreases as one ascends the atmosphere. If the density of air is \[\rho
\], what is the change in pressure \[dp\] over a differential height \[dh\]?
(b)
Considering the pressure p to be proportional to the density, find the pressure
p at a height h if the pressure on the surface of the earth is \[{{p}_{0}}\].
(c)
If \[{{\rho }_{0}}=1.03\times {{10}^{3}}\,N\,{{m}^{s}},\,\,{{\rho
}_{0}}=1.2\,kg\,{{m}^{-3}}\] and \[g=9.8\,m\,{{s}^{-2}},\] at what height will
the pressure drop to (1/10) the value at the surface of the earth?
(d)
This model of the atmosphere works for relatively small distances. Identify the
underlying assumption that limits the model.
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question_answer53)
Surface
tension is exhibited by liquids due to force of attraction between molecules of
the liquid. The surface tension decreases with increase in temperature and
vanishes at boiling point. Given that the latent heat of vaporization for water
\[{{L}_{v}}\,=\,540\,k\,cal\,\,k{{g}^{-1}},\] the mechanical equivalent of heat \[J=4.2\,J\,ca{{l}^{-1}},\]density
of water \[{{\rho }_{w}}=\,{{10}^{3}}\,kg\,{{l}^{-1}},\] Avagadro?s No \[{{N}_{A}}=6.0\times
{{10}^{26}}\,k\,mol{{e}^{-1}}\] and the molecular weight of water \[{{M}_{A}}=18\,kg\]
for 1 k mole.
(a)
Estimate the energy required for one molecule of water to evaporate.
(b)
Show that the inter-molecular distance for water is \[d={{\left[
\frac{{{M}_{A}}}{{{N}_{A}}}\times \,\frac{1}{\rho \omega } \right]}^{1/3}}\]
and find its
value.
(c)
1 g of water is the vapour state at 1 atm occupies \[1601\,c{{m}^{3}}\]. Estimate
the intermolecular distance at boiling point, in the vapour state.
(d)
During vaporization a molecule overcomes a force F, assumed constant, to go
from an inter-molecular distance d to d?. Estimate the value of F.
(e)
Calculate Fid, which is a measure of the surface tension.
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question_answer54)
A
hot air balloon is a sphere of radius 8 m. The air inside is at a temperature
of \[{{60}^{o}}C\]. How large a mass can the balloon lift when the outside
temperature is \[{{20}^{o}}C\]? (Assume air is an ideal gas\[R=8.314\,J\,mol{{e}^{-1}}\,{{K}^{-1}},\]
1 atm.
\[=1.013\times {{10}^{5}}\,Pa;\] the membrane tension is \[5\,N\,\,{{m}^{-1}}\].)
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