Mechanical Properties of Fluids Test

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Mechanical Properties of Fluids Test - 29

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Weekly Quiz Competition

Question 1
1 / -0

In a hydraulic machine, a force of $$2 N$$ is applied on the piston of area of cross section $$10 c{m}^{2}$$. What force is obtained on its piston of area of cross section $$100 c{m}^{2}$$?

A
20 N

B
10 N

C
5 N

D
40 N

Solution

We know that, $$Pressure = \dfrac{Force}{Area} $$
$$\Rightarrow Pressure = \dfrac{2}{10} = 0.2Ncm^{-2} $$
Now, $$Pressure = 0.2$$
Again, $$Force = Pressure \times Area$$
$$Force = 0.2 \times 100 = 20 N$$
Question 2
1 / -0

The diameter of neck and bottom of a bottle are $$2 cm$$ and $$10 cm$$ respectively. The bottle is completely filled with oil. If the cork in the neck is pressed in with a force of $$1.2 kgf$$, the amount of force applied on the bottom is

A
F= $$30$$ $$kgf$$

B
F=$$15$$ $$kgf$$

C
F = $$1.2 kgf$$

D
F=$$60$$ $$kgf$$

Solution

Radius of the cork at the neck is $$1 cm$$.
Area of the cork, $$A_{c}= \pi \times 1^2 cm^2$$
So, pressure applied through the cork, $$P_{c}=\dfrac{1.2}{\pi \times 1^2} kgf.{cm}^{-2}$$
Same pressure is applied on the bottom of the bottle as per Pascal's law.
Radius of the bottom of bottle is $$5 cm$$.
Area of the bottom, $$A_{b}= \pi \times 5^2 cm^2$$
So, force applied at the bottom = $$P_{c} \times A_{b}=\dfrac{1.2}{\pi \times 1^2} \times \pi \times 5^2=1.2 \times 25=30 kgf$$
Question 3
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A water tank of height $$10m$$, completely filled with water is placed on a level ground. It has two holes one at $$3 m$$ and the other at $$7 m$$ from its base. The water ejecting from:

A
both the holes will fall at the same spot

B
upper hole will fall farther than that from the lower hole

C
upper hole will fall closer than that from the lower hole

D
more information is required

Solution

Let $$h$$ be the height of the hole.
From Bernoulli's Theorem,
$$v=\sqrt{2g(10-h)}$$
This is the velocity of water from a hole at height $$h$$ from bottom.
Thus the range of the water from the hole=$$vt=\sqrt{2g(10-h)}\sqrt{\dfrac{2h}{g}}=2\sqrt{h(10-h)}$$
Thus it is same for $$h=3m$$ and $$h=7m.$$
Question 4
1 / -0

In a surface tension experiment with a capillary tube, water rises upto 0.1 m. If the same experiment is repeated in an artificial satellite revolving around the earth, then the water will rise in the capillary upto a height of

A
0.1 m

B
9.8 m

C
0.98 m

D
full length of capillary tube

Solution
Question 5
1 / -0

A tank is filled up to a height $$2\ H$$ with a liquid and is placed on a platform of height $$H$$ from the ground.The distance $$x$$ from the ground where a small hole is punched to get the maximum range $$R$$ is

A
$$H$$

B
$$1.25\ H$$

C
$$1.5$$

D
$$2\ H$$

Solution

Pressure at a height $$x=\rho g(3H-x)$$
Using Bernoulli's Equation inside and outside the hole,
$$\dfrac{1}{2}\rho v^2=\rho g(3H-x)$$
$$\implies v=\sqrt{2(3H-x)g}$$
Range of the liquid=$$vt=v\sqrt{\dfrac{2x}{g}}$$
$$=2\sqrt{x(3H-x)}$$
This is maximum for $$x=1.5H$$
Question 6
1 / -0

A spherical ball of density $$\rho $$ and radius $$0.003 m$$ is dropped into a tube containing a viscous fluid up to the $$0 \ cm$$ mark as shown in the figure. Viscosity of the fluid $$=1.26 N-s/m^{2}$$ and its density $$ \displaystyle \rho_{L} =\frac{\rho}{2}= 1260 kg/ m^{3}$$ Assume the ball reaches a terminal speed at $$10 cm$$ mark. The time taken by the ball to travel the distance between the $$10 cm$$ and $$20 cm $$ mark is $$(g = 10m/s ^{2} )$$

A
$$2 s$$

B
$$1 s$$

C
$$0.5 s$$

D
$$5 s$$

Solution

$$\displaystyle v_{T}=\frac{2}{9}\frac{r^{2}\left ( \rho -\sigma \right )g}{\eta }$$
$$\displaystyle =\frac{2\times \left ( 0.003 \right )^{2}\left ( 1260\times 2-1260 \right )\times 10}{9\times 1.26}$$
$$=0.02$$ m/s
$$\displaystyle t=\frac{d}{v_{T}}=\frac{10\times 10^{-2}}{0.02}=5$$ s
Question 7
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Directions For Questions

The spouting can is something used to demonstrate the variation of pressure with depth. When the corks are removed from the tubes in the side of the can, water flows out with a speed that depends on the depth. In a certain can, three tubes $$T_{1},T_{2}$$ and $$T_{3}$$ are set at equal distances a above the base of the can. When water contained in this can is allowed to come out of the tubes the distances on the horizontal surface are measured as $$x_{1},x_{2}$$ and $$x_{3}$$

...view full instructions

Speed of efflux is

A
$$\sqrt{3gh}$$

B
$$\sqrt{2gh}$$

C
$$\sqrt{gh}$$

D
$$\displaystyle \frac{1}{2} \sqrt{2gh}$$

Solution

Applying Bernoulli's Theorem inside and outside the hole,
$$P_{inside}+\dfrac{1}{2}\rho (0)^2+\rho gH=P_{outside}+\dfrac{1}{2}\rho v ^2+\rho gH$$
Thus $$P_0+\rho gh=P_0+\dfrac{1}{2}\rho v^2$$
$$\implies v=\sqrt{2gh}$$
Question 8
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A large open tank has two holes in the wall. One is a square hole of side $$L$$ at a depth h from the top and the other is a circular hole of radius $$R$$ at a depth $$4 h$$ from the top, When the tank is completely filled with water, quantities of water flowing out per second from both holes are the same. Then $$R$$ is equal to

A
$$\displaystyle \frac{L}{\sqrt{2 \pi}}$$

B
$$2/\pi L$$

C
$$L$$

D
$$\displaystyle \frac{L}{2 \pi}$$

Solution

Since the water quantity from both the holes are equal, we have
$$a_1v_1=a_2v_2$$
$$\Rightarrow L^2\sqrt{2gy}=\pi R^2\sqrt{2g(4y)} \because$$ velocity of efflux at depth h is given by $$v =\sqrt{2gh}$$
$$\Rightarrow R=\frac{L}{\sqrt{2\pi}}$$
Question 9
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Three points $$A, B$$ and $$C$$ on a steady flow of a non viscous and incompressible fluid are observed. The pressure, velocity and height of the points $$A, B $$ and $$C$$ are $$(2,3, 1). (1, 2, 2)$$and $$(4, 1, 2)$$ respectively. Density of the fluid is $$1 kgm^{-3}$$ and all otner parameters are given in SI units. Then which of the following is correct? $$(g = 10 ms ^{-2})$$

A
points A and B lie on the same stream line

B
point B and C lie on same stream line

C
point C and A lie on same stream line

D
None of the above

Solution

Given : $$\rho = 1 kg/m^3$$
Using Bernoulli's theorem, $$P + \rho gh + \dfrac{1}{2} \rho v^2 =constant$$
For point A : $$2 + 1 (10) (1) + \dfrac{1}{2} \times (1) (3^2) =16.5$$

For point B : $$1 + 1 (10) (2) + \dfrac{1}{2} \times (1) (2^2) =23$$

For point C : $$4 + 1 (10) (2) + \dfrac{1}{2} \times (1) (1^2) = 24.5$$
As the value of the constants are different in each case, thus all these points do not lie on same stream line.
Question 10
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Two cylindrical vessels fitted with pistons A and B of area of cross section $$8 c{m}^{2}$$ and $$320 c{m}^{2}$$ respectively, are joined at their bottom by a tube and they are completely filled with water. Find : (i) the pressure on piston A, (ii) the pressure on piston B, and (iii) the thrust on piston B.(consider effort on piston A $$E=4kgf$$)

A
(i) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$160$$ $$kgf$$

B
(i) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$16$$ $$kgf$$

C
(i) $$10$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$10$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$160$$ $$kgf$$

D
(i) $$0.5$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$0.5$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$160$$ $$kgf$$

Solution

Let $$E$$ be the effort applied on the smaller piston $$A $$ and $$ L$$ be the load required on the larger piston $$B$$.
Area of cross section of pistion $$A = 8 cm^{2}$$
Area of cross section of pistion $$A = 320 cm^{2}$$
(i) Pressure acting on piston $$A$$ in the downward direction $$= Thrust/Area = E/8 = 4/8 = 0.5$$
$$ \therefore$$Pressure acting on water $$= E/8 =0.5$$ (according to Pascal's Law)
(ii) $$\therefore$$ Pressure acting on piston $$B = E/8 =0.5$$ (according to Pascal's Law)
(iii) Thrust acting on piston B in the upward direction $$= Pressure \ \ \times Area \ \ of B$$

$$ = \dfrac{E \times 320}{8} = 160 $$

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Mechanical Properties of Fluids Test - 29

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Mechanical Properties of Fluids Test - 29

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Question 1

20 N

10 N

5 N

40 N

Solution

Question 2

F= $$30$$ $$kgf$$

F=$$15$$ $$kgf$$

F = $$1.2 kgf$$

F=$$60$$ $$kgf$$

Solution

Question 3

both the holes will fall at the same spot

upper hole will fall farther than that from the lower hole

upper hole will fall closer than that from the lower hole

more information is required

Solution

Question 4

0.1 m

9.8 m

0.98 m

full length of capillary tube

Solution

Question 5

$$H$$

$$1.25\ H$$

$$1.5$$

$$2\ H$$

Solution

Question 6

$$2 s$$

$$1 s$$

$$0.5 s$$

$$5 s$$

Solution

Question 7

$$\sqrt{3gh}$$

$$\sqrt{2gh}$$

$$\sqrt{gh}$$

$$\displaystyle \frac{1}{2} \sqrt{2gh}$$

Solution

Question 8

$$\displaystyle \frac{L}{\sqrt{2 \pi}}$$

$$2/\pi L$$

$$L$$

$$\displaystyle \frac{L}{2 \pi}$$

Solution

Question 9

points A and B lie on the same stream line

point B and C lie on same stream line

point C and A lie on same stream line

None of the above

Solution

Question 10

(i) $$5$$ $$kgf$$ $$c{m}^{-2}$$(ii) $$5$$ $$kgf$$ $$c{m}^{-2}$$(iii) $$160$$ $$kgf$$

(i) $$5$$ $$kgf$$ $$c{m}^{-2}$$(ii) $$5$$ $$kgf$$ $$c{m}^{-2}$$(iii) $$16$$ $$kgf$$

(i) $$10$$ $$kgf$$ $$c{m}^{-2}$$(ii) $$10$$ $$kgf$$ $$c{m}^{-2}$$(iii) $$160$$ $$kgf$$

(i) $$0.5$$ $$kgf$$ $$c{m}^{-2}$$(ii) $$0.5$$ $$kgf$$ $$c{m}^{-2}$$(iii) $$160$$ $$kgf$$

Solution

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(i) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$160$$ $$kgf$$

(i) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$5$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$16$$ $$kgf$$

(i) $$10$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$10$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$160$$ $$kgf$$

(i) $$0.5$$ $$kgf$$ $$c{m}^{-2}$$

(ii) $$0.5$$ $$kgf$$ $$c{m}^{-2}$$

(iii) $$160$$ $$kgf$$