Mechanical Properties of Fluids Test

Result

Mechanical Properties of Fluids Test - 63

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Question 1
1 / -0

An air bubble rises from the bottom of a lake to the surface if its radius increases by 200% and atmospheric pressure are equal to a water column of height H, then depth of the lake is (assume Temperature to be constant at top and bottom of the lake)

A
21 H

B
8 H

C
9 H

D
26 H

Solution
Question 2
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Calculate the mass of lead which will be required to just submerge in water a block of wood weighing $$50$$ g (a) when lead is attached underneath, (b) when lead is placed on the top of the block. Take sp. gravity of lead = $$11.3$$ and of wood = $$0.75$$.

A
(a) $$ 28.28$$ g
(b) $$16.67$$ g

B
(a) $$ 18.28$$ g
(b) $$26.67$$ g

C
(a) $$ 18.28$$ g
(b) $$16.67$$ g

D
(a) $$ 18.28$$ g
(b) $$50.67$$ g

Solution
Question 3
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The pressure exerted by a force of $$50 \ N$$, normal to the nail of area $$1 \ mm^2$$ is

A
$$5 \times 10^7$$ Pa

B
$$5 \times 10^6$$ Pa

C
$$5 \times 10^5$$ Pa

D
$$5 \times 10^4$$ Pa

Solution

Given:
Force $$F=50 \ N$$
Area $$A= 1 \ mm^2=(10^{-3} \ m) \times (10^{-3} \ m)=10^{-6} \ m^2 $$

We know that,
Pressure $$P=\dfrac{F}{A}=\dfrac{50}{10^{-6}}=5 \times 10^7 \ N/m^2$$
Also, $$1 \ N/m^2= 1 \ Pa$$
So pressure $$P=5 \times 10^7 \ Pa$$

Answer: $$(A)$$
Question 4
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A stream of water escapes from a hole $$2\ m$$ above the base of a tank and strikes the ground at a horizontal distance of $$6\ m$$. The depth of the hole from the free surface of water is

A
$$4\ m$$

B
$$4.5\ m$$

C
$$9\ m$$

D
$$6\ m$$

Solution

$$H=\text { height of Beaker } \\$$
$$h=\text { height of hole from Bottom } \\$$
$$R=6 \mathrm{~m} \\$$
$$\text { We know that }$$

$$R=\sqrt{4 h(H-h)} \\$$
$$6=\sqrt{4 \times 2(H-2)} \\ $$
$$36=8(H-2) \\$$
$$(H-2)=4.5$$

height of hole from

Surface $$=4.5 \mathrm{~m}$$

Answer:-(B)
Question 5
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There is a hole at the bottom of a large open vessel. If water is filled upto a height $$h$$, it flows out in time $$t$$. If water is filled to a height $$4h$$, it will flow out in time.

A
$$\dfrac {t}{3}$$

B
$$\dfrac {t}{4}$$

C
$$3t$$

D
$$2t$$

Solution

$$\text { We know that } \\$$
$$V_{i}=\sqrt{2 g h} \\$$
$$\text { and } \\$$
$$V_{f}=0$$

$$\text { so } \\$$
$$V_{f}=V_{i}-g t \\$$
$$V_{i}=g t$$

$$t=\sqrt{\frac{2 h}{g}}$$

$$t_{2}=\sqrt{\frac{2 \times 4 h}{g}}$$

$$t_{2}=2 t$$

Answer:- $$(D)$$
Question 6
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A water tank is filled with water up to a height $$8 \:m$$ a hole is made in the tank wall at a depth $$3\: m$$ from the surface of water. Then the time taken to reach the ground

A
$$1 sec$$

B
$$2 sec$$

C
$$3 sec$$

D
$$4 sec$$

Solution
Question 7
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Directions For Questions

In a cylindrical container of sufficiently large height, two easily moving pistons enclose certain amount of same ideal gas in two chambers as shown in the figure.The upper piston is at a height 20 cm from the bottom and lower piston is at a height 8 cm from the bottom.The mass of each piston is m kg and cross sectional area of each piston is $$A\, m^2$$, where $$\dfrac{mg}{A}=P_0$$ and $$P_0$$ is the atmospheric pressure =$$1 \times 10^5 N/m^2$$.
The cylindrical container and pistons are made of conducting material.Initially the temperature of gas is $$27^0C$$ and whole system is in equilibrium. Now if the upper piston is slowly lifted by $$16\ cm$$ and held in that position with the help of some external force.As a result, the lower piston rises slowly by $$l\ cm$$.

...view full instructions

The value of $$l$$ is

A
$$2\ cm$$

B
$$4\ cm$$

C
$$8\ cm$$

D
$$6\ cm$$
Question 8
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A water tank is filled with water up to a height H hole is made in the tank wall at a depth h from the aurface of water. Then the volcity of efflux

A
$$\sqrt{gh}$$

B
$$\sqrt{2gh}$$

C
$$2 gh$$

D
$$pgh$$

Solution

Acc. to bernoulli's Theorem.
$$P_{0}+\rho g H+0=P_{0}+0+\frac{1}{2} \rho v^{2}$$
So, $$v=\sqrt{2 g H}$$
Answer: $$(B) \sqrt{2 g h}$$
Question 9
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Given figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height $$h_0$$ and pressure $$2P_0$$ where $$P_0$$ is the atmospheric pressure. There is a hole in the wall of the tank at a depth $$h_1$$ below the top from which water comes out. A long vertical tube is connected as shown
Find the height $$h_2$$ of the water in the long tube above the top initially

A
$$\dfrac{3P_0}{\rho g} - \dfrac{h_0}{3}$$

B
$$\dfrac{2P_0}{\rho g} - \dfrac{h_0}{2}$$

C
$$\dfrac{P_0}{\rho g} - h_0$$

D
$$\dfrac{P_0}{2\rho g} - 2h_0$$

Solution
Question 10
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The given table shown properties of four cells system $$A, B, C$$ and $$D$$. The maxium rate of inward diffusion of water will be observed in which of these system?
System Intracellular concentration
of water Extracellular concentration
of water
A 0.09M 0.11M
B 0.2 M 0.5 M
C 0.05M 0.7M
D 0.03M 0.6M

A
System A

B
System B

C
System C

D
System D

Solution