Mechanical Properties of Fluids Test

Result

Mechanical Properties of Fluids Test - 65

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Question 1
1 / -0

In a cylindrical vessel containing liquid of density $$p$$, there are two holes in the side wall at heights $$h_{1}$$ and $$h_{2}$$ respectively such that the range of efflux at the bottom of the vessel is same. The height of a hole, for which the range of efflux would be maximum, will be:

A
$$(h_{2}-h_{1})$$

B
$$\dfrac{h_{2}-h_{1}}{2}$$

C
$$h_{1}+h_{2}$$

D
$$\dfrac{h_{1}+h_{2}}{2}$$

Solution

let height of vessel = H.
from, Bernoulli's theorem.
velocity of liquid at $$h_{1} ,V_{1}=\sqrt{2 g\left(H-h_{1}\right)}$$
Range $$R_{1}=v_{1} t$$
for $$t$$,
$$h_{1}=\frac{1}{2} \times g \times t^{2}$$
$$t=\sqrt{\frac{2 h_{1}}{g}}$$
$$R_{1}=V_{1} t=2 \sqrt{(H-h)} h_{1}$$
For $$h_{2}$$ height, Range $$R_{2}=2 \sqrt{\left(H-h_{2}\right) h_{2}}$$
$$\because R_{1}=R_{2}$$
$$2 \sqrt{\left(H-h_{1}\right) h_{1}} =2 \sqrt{\left(H-h_{2}\right) h_{2}}$$
0r
$$H\left(h_{1}-h_{2}\right)=\left(h_{1}+h_{2}\right)\left(h_{1}-h_{2}\right)$$
Or
$$H=h_{1}+h_{2}$$
now, let $$h_{1}$$ height is $$'y'$$ height below than $$'H'$$
$$R=2 \sqrt{(H-y) y}$$
$$\dfrac{d R^{2}}{d y}=\dfrac{d}{d y}\left(H y-y^{2}\right)$$
$$\quad$$
$$\quad H-2 y=0$$
or $$y=H / 2$$
for $$\max$$ value $$y=\dfrac{h_{1}+h_{2}}{2}$$
Correct option is (D).
Question 2
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At $$20^{o} $$C, to attain the terminal velocity how fast will an aluminium sphere of radii $$1\ mm$$ fall through water. Assume flow to be laminar flow and specific gravity $$(Al)-2.72$$

A
$$5\ m/s$$

B
$$4.6\ m/s$$

C
$$4\ m/s$$

D
$$2\ m/s$$

Solution
Question 3
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Water flows through a horizotal pipe of varying cross-section. The pressure of water equals to 0.1 m of mercury at a place where the velocity of flow is 0.4 $$ms^{-1}$$. What will be the pressure at another place where the velocity of flow is 0.5 $$ms^{-1}$$?

A
0.08966 m of Hg column.

B
0.09966 m of Hg column.

C
0.09977 m of Hg column.

D
0.09999 m of Hg column.

Solution
Question 4
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Water flows in a streamline manner through a capillary tube of radius a. The pressure difference being P/2 and the rate of flow is 8 cc per second. If the radius is reduced to r/2 and the pressure is increased to P, then the rate of flow becomes

A
1 CC/S

B
2 CC/S

C
4 CC/S

D
8 CC/S

Solution
Question 5
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Two equal spherical bodies A and B specific gravity $$1.2$$ and $$0.8$$ respectively are attached by a thin mass less rod. Now it is placed inside the water as shown in the figures. The bodies A and B are in

A
stable equilibrium

B
unstable equilibrium

C
neutral equilibrium

D
information is inadequate

Solution
Question 6
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A vision liquid flows through a horizontal pipe of varying cross-sectional area. Identify the option which correctly represents the variation of height of rise of liquid in each vertical tube

A

B

C

D
None of these

Solution
Question 7
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A wooden cylinder of diameter $$4r$$, height $$h$$ and density $$\rho /3$$ is kept on a hole of diameter $$2r$$ of tank, filled with liquid of density $$\rho$$ as shown in the figure.
Now level of the liquid starts decreasing slowly. When the level of liquid is at a height $${h}_{1}$$ above the cylinder the block starts moving up. At what value of $${h}_{1}$$, will the block rise?

A
$$4h/9$$

B
$$5h/9$$

C
$$5h/3$$

D
Remains same

Solution
Question 8
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Bernoulli's equation is applicable to

A
Static fluids

B
Flowing liquids

C
Energy of liquid

D
Both 1&3

Solution

Bernoulli's equation is applicable for flowing liquids.
Option is (B).
Question 9
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A metal ball is being weighed in a liquid whose temperature is raised continuously. Then the apparent weight of the ball :

A
remain unchnaged

B
increases

C
decreases

D
changes erratically

Solution
Question 10
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When a pipe of the radius of cross- section '$$r$$' is arranged at a height h horizontally the jet of from it touches at a distance '$$x$$' from a point just below the pipe on the ground. if the pipe is closed partly such that its radius of cross-section becomes $$r/2$$ and it is arranged at a height $$4h$$ then the horizontal distance at which waterfall increases by

A
$$8x$$

B
$$2x$$

C
$$7x$$

D
$$x/2$$

Solution