Mechanical Properties of Fluids Test

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Mechanical Properties of Fluids Test - 52

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Question 1
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When water is flowing through a pipe with a speed $$v$$, then its power is proportional to

A
$$v^{2}$$

B
$$v^{3/2}$$

C
$$v^{3}$$

D
$$\sqrt {v}$$

Solution

Using Bernoulli's equation.
Energy per unit volume before $$=$$ Energy per unit volume after
$${ p }_{ 1 }+\dfrac { 1 }{ 2 } { pv }_{ 1 }^{ 2 }+{ pgh }_{ 1 }={ p }_{ 2 }+\dfrac { 1 }{ 2 } { pv }_{ 2 }^{ 2 }+{ pgh }_{ 2 }$$
$${ A }_{ 2 }<{ A }_{ 1 }$$
$${ V }_{ 2 }>{ V }_{ 1 }$$
$${ p }_{ 2 }<{ p }_{ 1 }$$
Hence power $$\alpha { v }^{ 2 }$$.
Question 2
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A container of height $$10\ cm$$ is filled with water. There is a hole at bottom. Find the pressure difference between points $$A$$ & $$B$$.

A
$$1000\ Pa$$

B
Zero

C
$$1\ Pa$$

D
$$100\ Pa$$

Solution

$$P_{A} - P_{B} = \rho gh$$
$$= 10^{3} \times 10\times 10\times 10^{-2} Pa$$
$$= 1000\ Pa$$.
Question 3
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A block of sided $$0.5 m$$ is $$30\%$$ submerged in a liquid of density $$1 \, gm/cc$$. Then find mass of an object placed on block for complete submergence.

A
$$87.3 kg$$

B
$$85.3 kg$$

C
$$82.3 kg$$

D
$$80.3 kg$$

Solution

Initial condition $$B = mg$$

$$\rho\dfrac{3}{10}Vg = mg$$. ...(1)

$$\rightarrow (1000 \,kg/m^3) \dfrac{3}{10} (0.5m)^3 = m$$

$$m = 37.5 \,kg$$
finally $$\rho vg = (m + M)g$$ ...(2)
From equation (1) & (2)

$$\dfrac{(m + M)g}{mg} = \dfrac{\rho Vg}{\rho\dfrac{3}{10}Vg}$$

$$1 + \dfrac{M}{m} = \dfrac{10}{3}$$

$$\dfrac{M}{m} = \dfrac{7}{3}$$

$$\dfrac{M}{m} = \dfrac{7}{3}$$

$$M = \dfrac{7}{3} (37.5)kg = 87.3 \,kg$$
Question 4
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A steel ball is dropped in a viscous liquid. The distance of the steel ball from the top of the liquid is shown below. The terminal velocity of the ball is closest to :

A
$$0.26 m/s$$

B
$$0.33 m/s$$

C
$$0.45 m/s$$

D
$$0.21 m/s$$

Solution

For terminal velocity, slope should be constant. If we look carefully slope is constant from $$t=1.6\ sec$$ to $$t=2\ sec$$

$$V_t=\dfrac{0.4-0.3}{2-1.6}=\dfrac{0.1}{0.4}=0.25\ m/s$$

So terminal velocity is closest to $$0.26\ m/s$$
Question 5
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The working of venturimeter is based on

A
Torricelli's law

B
pascal's law

C
Bernoulli's theorem

D
Archimede's principle

Solution
Question 6
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The density of Saturn is $$ 687 kg/m^3 $$. It is kept in a lake filled with water. Then:

A
It will float in water

B
It will get submerged in water completely and sink to the bottom of the lake

C
It will get submerged in water completely but will not sink to the bottom

D
None of these

Solution
Question 7
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Venturimetre is used to measure

A
Flow speed of a fluid

B
Atmospheric pressure

C
Specific gravity

D
Pressure in a closed vessel

Solution
Question 8
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A film of water is formed between two straight parallel wires each $$10\mathrm { cm }$$ long and at separation $$0.5\mathrm { cm } .$$ Calculate the work required to increase $$1\mathrm { mm }$$ distance between the wires. Surface tension of water $$= 72 \times 10 ^ { - 3 } \mathrm { N } / \mathrm { m } .$$

A
$$1.44 \times 10 ^ { - 3 }$$

B
$$1.44 \times 10 ^ { - 7 }$$

C
$$1.44 \times 10 ^ { - 5 }$$

D
$$1.44 \times 10 ^ { - 4 }$$

Solution

Given:
Length $$L=10$$ cm
Width $$W=0.5$$ cm
Surface tension $$S=72 \times { 10^{ -3 }}$$
Increase distance by $$\Delta l=1$$ mm
change in area $$\Delta A=(L\times W)=10(.1)\times 10^{-4}$$

$$\begin{array}{l} E=S\Delta A \\ =72\times { 10^{ -3 } }\times 2\times 1\times { 10^{ -4 } } \\ =1.44\times { 10^{ -5 } }J \\ Ans.\, \, (C) \end{array}$$
Question 9
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Calculate the energy spent in spraying a drop of mercury of radius $$R$$ into $$n$$ droplets
all of same size. Given the surface tension of mercury is $$T .$$

A
$$4 \pi R ^ { 2 } T \left( n ^ { 1 / 3 } - 1 \right)$$

B
$$4 \pi r ^ { 2 } T \left( n ^ { 1 / 3 } - 1 \right)$$

C
$$4 \pi r ^ { 2 } \left( n ^ { 1 / 3 } - 1 \right)$$

D
None of these

Solution

$$\begin{array}{l} n\cdot \frac { 4 }{ 3 } \pi { r^{ 3 } }=\frac { 4 }{ 3 } \pi { R^{ 3 } } & \\ \Rightarrow n{ r^{ 3 } }={ R^{ 3 } } & ...(i) \\ E=\left( { n\cdot 4\pi { r^{ 2 } }-4\pi { R^{ 2 } } } \right) T & \\ =4\pi T\left( { n\cdot { { \left( { \frac { { { R^{ 3 } } } }{ n } } \right) }^{ \frac { 2 }{ 3 } } }-{ R^{ 2 } } } \right) & \\ =4\pi T{ R^{ 2 } }\left( { { n^{ 1/3 } }-1 } \right) & \\ Ans.\, (A) & \end{array}$$
Question 10
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A flask containing air at $$27^oC$$ at atmospheric pressure is croked up. A pressure of $$2.5\ atm$$, inside the flask would force the rock out. The temperature at which it will happen is :

A
$$67.5^oC$$

B
$$577^oC$$

C
$$670^oC$$

D
$$750\ K$$

Solution