Mechanical Properties of Fluids Test

Result

Mechanical Properties of Fluids Test - 49

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Question 1
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Water enters a horizontal pipe of non uniform cross section with a velocity of $$0.4$$ $$m s ^ { - 1 }$$ and leaves the other end with a velocity of $$0.6$$ $$m s ^ { - 1 }$$ .pressure of water at the first end is $$1500$$ $$N m ^ { - 2 }$$,then pressure at the other end is

A
$$1000$$ $$N m ^ { - 2 }$$

B
$$1200$$ $$N m ^ { - 2 }$$

C
$$1400$$ $$N m ^ { - 2 }$$

D
$$1600$$ $$N m ^ { - 2 }$$

Solution

Bernoulli's equation for a horizontal pipe can be used to find the pressure at the second point of the pipe, which is

$$\dfrac 12 \rho V_1^2+P_1=\dfrac 12\rho V_2^2+P_2$$

where

$$\rho$$ is the density of the water $$=1000kg/m^3$$

$$V_1$$ is the velocity at first point $$=0.6\,m/s$$

$$P_1$$ is the pressure at first point $$=1500N/m^2$$

$$V_2$$ is the velocity of second point $$=0.4m/s$$

$$P_2$$ is the pressure at second point $$=?$$

Putting these values in the Bernoulli's equation,

$$\dfrac 12(1000)(0.6)^2+1500=\dfrac 12(1000)(0.4)^2+P_2$$

$$P_2=500[(0.6)^2-(0.4)^2]+1500=1600\,Nm^{-2}$$
Question 2
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Directions For Questions

A cylindrical tank having cross sectional area $$A=0.5\ m^{2}$$ is filled with tow liquids of density $$p_1=900\ kgm^-3\ and p_2=600\ kgm^{-3}$$ to a height $$h=60\ cm$$ each as shown in figure.

...view full instructions

Velocity of efflux

A
$$1\ ms^{-1}$$

B
$$2\ ms^{-1}$$

C
$$3\ ms^{-1}$$

D
$$4\ ms^{-1}$$

Solution

In the given figure,
$$\begin{array}{l} 600\, ks/{ m^{ 3 } }\, \, \, -\, \, 60cm \\ 900\, ks/{ m^{ 3 } }\, \, \, -\, \frac { { 60\times 2 } }{ 3 } =40\, cm \\ v=\sqrt { 2gh } \\ =\sqrt { 2\times 10\times \frac { { 80 } }{ { 100 } } } \\ =4\, m{ s^{ -1 } } \end{array}$$
So,
Option $$D$$ is correct answer.
Question 3
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A drop of liquid having radius 2 cm has a terminal velocity 20 cm/sec, the terminal velocity of a drop of 1 mm radius will be :

A
40 cm/s

B
20 cm/s

C
10 cm/s

D
5 cm/s

Solution
Question 4
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Eight equal drops of water each if radius $$r=2\ mm$$ are falling through air with a terminal velocity of $$16\ cm/s$$. The eight drops combine to form a big drop. Calculate the terminal velocity of big drop

A
$$16\ cm/s$$

B
$$32\ cm/s$$

C
$$64\ cm/s$$

D
None of these

Solution
Question 5
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A cylinder with a movable piston contains air under a pressure $${ p }_{ 1 }$$ and a soap bubble of radius 'r' The which the air should be compressed by slowly pushing the pistc size by half will be: ( The surface tension is S, and temperature T is malntalned constant)

A
$$\left[ { 8p }_{ 1 }+\dfrac { 24S }{ r } \right] $$

B
$$\left[ { 4p }_{ 1 }+\dfrac { 24S }{ r } \right] $$

C
$$\left[ { 2p }_{ 1 }+\dfrac { 24S }{ r } \right] $$

D
$$\left[ { 2p }_{ 1 }+\dfrac { 12S }{ r } \right] $$

Solution
Question 6
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A beaker containing water is placed on the platform of a spring balance. The balance reads $$1.5kg$$. A stone of mass $$0.5kg$$ and density $$500kg/{m}^{3}$$ is completely immersed in water without touching the walls of the beaker. What will be the balance reading now?

A
$$2kg$$

B
$$2.5kg$$

C
$$1kg$$

D
$$3kg$$

Solution
Question 7
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The volume of an air bubble increases by $$x$$% as it raises from the bottom of a water lake to its surface. If the water barometer reads $$H$$. The depth of the lake is :

A
$$ \dfrac {H}{100x} $$

B
$$ \dfrac {Hx}{100} $$

C
$$ Hx \times 100 $$

D
$$ \dfrac {H}{x}100 $$

Solution
Question 8
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A solid cone of height $$H$$ and base radius $$H/2$$ floats in a liquid of density $$\rho$$. It is hanging from the ceiling with the help of a string. The force by the fluid on the curved surface of the cone is ($${P}_{0}=$$ atmospheric pressure)

A
$$\pi{H}^{2}\left( \cfrac { { P }_{ 0 } }{ 4 } +\cfrac { \rho gH }{ 3 } \right) $$

B
$$\pi{H}^{2}\left( \cfrac { { P }_{ 0 } }{ 4 } +\cfrac { \rho gH }{ 6 } \right) $$

C
$$\cfrac{\pi{H}^{2}}{4}\left( \cfrac { { P }_{ 0 } }{ 4 } + { \rho gH }{ } \right) $$

D
$$\cfrac{\pi{H}^{2}}{4}\left( { { P }_{ 0 } }{ } + { \rho gH }{ } \right) $$

Solution
Question 9
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Water is poured from a height of 10 m into an empty barrel at the rate of 1 litre per second. If the weight of the barrel is 10 kg, the weight indicated at time t = 60 s will be

A
$$71.4 \mathrm { kg }$$

B
$$68.6 \mathrm { kg }$$

C
$$70.0 \mathrm { kg }$$

D
$$84.0 \mathrm { kg }$$

Solution

Time taken to reach $$10m$$ below $$=\sqrt {\dfrac{{2 \times 10}}{{10}}} = \sqrt 2 \,\sec $$
$$\therefore $$ only $$\left( {60 - \sqrt 2 } \right)\sec $$ is effective for pouring of water
$$\therefore $$ total weight $$=10lkg+\left( {60 - \sqrt 2 } \right)l \times \dfrac{{1\,kg}}{l}$$
$$=58.6kg+10kg$$
$$=68.6kg$$
Hence,
option $$(B)$$ is correct answer.
Question 10
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The radius of one arm of a hydraulic lift is three times the radius of the other arm. What force should be applied on the narrow arm so as to lift $$50kg$$ at the wider arm?

A
60 N

B
55.6 N

C
26.7 N

D
30 N

Solution