Force and Pressure Test

Result

Force and Pressure Test - 6

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Question 1
1 / -0

The density of air is 1.3 kg/m³. What mass of air is contained in a room measuring 2.5 m x 4 m x 10 m?

A
100 kg

B
130 kg

C
160 kg

D
180 kg

Solution

Density = Mass / Volume
Mass = Density x Volume
Here Volume , V = 2.5 x 4 x 10
M = 1.3 x (2.5 x 4 x 10) = 130 kg
Question 2
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Equal masses of two liquids having densities D and 2D are mixed, then the density of the resulting mixture is

A
D

B

C

D

Solution

Density of mixture = Total Mass / Total Volume
If V₁ and V₂ is the volume of two liquids, then

and
Question 3
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The densities of three liquids are D, 2D and 3D. What will be the density of the resulting mixture if equal volume of the three liquids are mixed?

A
6D

B
1.4D

C
2D

D
3D

Solution

Density of the mixture

Let M₁, M₂ and M₃ are the masses of three liquids.
Question 4
1 / -0

Two vessels A and B have the same base area and contain water up to the same height, but the mass of water in vessel A is four times that of water in vessel B. The ratio of pressure on the base of vessel A to that on the base of vessel B is

A
4 : 1

B
2 : 1

C
1 : 1

D
16 : 1

Solution

Pressure due to liquid column is given by:
P = ρgh, where h is the height and ρ is the density of the liquid.
Hence, pressure depends only of the height of the liquid column and is independent of the shape of the vessel and the mass of the liquid.
So, pressure on the base of both the vessels (A and B) is the same. So, the required ratio is 1 : 1.
Question 5
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Read the following statements and choose the correct option.

Statement A: At the bottom of three vessels having different shapes, if the water is filled up to the same height, the pressure is the same.

Statement B: Pressure is independent of the base area and depends on the height of the liquid filled.

A
Both statements A and B are correct and B is the correct explanation of A.

B
Both statements A and B are correct.

C
B is not the correct explanation of A.

D
Statement A is incorrect, but statement B is correct.

E
Both statements A and B are incorrect.

Solution

Both statements A and B are correct and B is the correct explanation of A.
Pressure exerted by the liquid column is given by
P = ρgh
So, it is independent of the base area and shape of the vessel and depends upon the height of the liquid column and density of the liquid so as all vessels are filled with same liquid to same height, pressure at the bottom of the vessels will be same.
Question 6
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In which of the following cases will the increase in pressure be the greatest?

A
When the force acting is increased and the area is also increased.

B
When the force acting is increased but the area is decreased.

C
When the force acting is decreased and the area is also decreased.

D
When the force acting is decreased but the area is increased.

Solution

Pressure = Force / Area
So, when the force acting is increased but the area is decreased, pressure will increase.
Question 7
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Read the following statements and choose the correct option.

Statement A: At the mountains, the water boils at a temperature less than 100°C.
Statement B: At the top of mountains, the atmospheric pressure is less than pressure at sea-level.

A
Both statements A and B are correct and B is the correct explanation of A.

B
Both statements A and B are correct, but B is not the correct explanation of A.

C
Statement A is incorrect, but statement B is correct.

D
Both statements A and B are incorrect.

Solution

Both statements A and B are correct and B is the correct explanation of A.
Boiling point is the temperature at which the vapour pressure becomes equal to the atmospheric pressure. At mountains the atmospheric pressure is less, so the boiling point of the water is less than 100^oC.
Question 8
1 / -0

Choose the correct statements from the following.

(A) Blood pressure is minimum at our feet and maximum at our head.
(B) It is easier for a camel to move on the sand because its feet have a large area.
(C) The pressure along a horizontal line in a vessel filled with water is the same.

A
Only (A) and (B)

B
Only (A) and (C)

C
Only (B) and (C)

D
All of them are correct.

Solution

Blood pressure is maximum at our feet and minimum at our head.
It is easier for a camel to move on the sand because its feet have a large area and exert less pressure due to which they do not sink in the sand.
The pressure along a horizontal line in a vessel at rest, filled with water is the same.
Question 9
1 / -0

Choose the correct relationship between pressures exerted at points A, B and C in the liquid.

A
P_A = P_B= P_C

B
P_A > P_B> P_C

C
P_A < P_B< P_C

D
P_A > P_B= P_C

Solution

For the liquid at rest, along the horizontal line the pressure is always same. Hence, P_A = P_B= P_C
Question 10
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The given blocks A, B and C, all having the same density are immersed in a fluid. For which of these blocks is the buoyant force the greatest?

A
B

B
C

C
A

D
Cannot be determined

Solution

As the buoyant force is defined as the weight of the liquid displaced.
Buoyant force = Density of the liquid × Volume of the liquid displaced × Acceleration due to gravity
Hence, greater is the volume displaced, greater is the buoyant force.
Question 11
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Which of the following options is/are TRUE?

A
Magnitude of buoyant force is maximum when the object is fully immersed in the liquid.

B
Magnitude of buoyant force increases as the density of the liquid decreases.

C
Magnitude of buoyant force is minimum when the object is fully immersed in the liquid.

D
Both (1) and (2)

Solution

Buoyant force is defined as the weight of the liquid displaced.
Buoyant force = Density of the liquid x Volume of the liquid displaced x Acceleration due to gravity
Hence, greater is the volume displaced, greater is the buoyant force. Volume displaced will be maximum when it is fully immersed. Greater is the density of the liquid, greater is the buoyant force.
Question 12
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Read the following statements and choose the correct option.

Statement A: Buoyant force on a fully immersed sphere will be more than that on a cube which is made of the same material and has the same mass as the sphere.
Statement B: Sphere will displace less volume as compared to the cube.

A
Both statements A and B are correct and B is the correct explanation of A.

B
Both statements A and B are correct, but B is not the correct explanation of A.

C
Statement A is incorrect, but statement B is correct.

D
Both statements A and B are incorrect.

Solution

Volume of the sphere will be less as compared to the cube hence it will displace less liquid in which it is immersed, so it will experience less buoyant force.
Question 13
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A solid piece of iron sinks in water but floats in mercury. This is because the

A
average density of water and mercury is less than that of iron

B
density of iron is more than that of water as well as mercury

C
density of iron is less than that of water as well as mercury

D
density of iron is more than that of water but less than that of mercury

Solution

The object will float in liquid if its density is less than the liquid in which it is immersed so density of iron is more than that of water but less than that of mercury.
Question 14
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A sphere made of iron is immersed in water. Another sphere of same dimensions but made of aluminium is immersed in alcohol. Choose the correct statement from the following.

A
Both spheres will experience the same buoyant force.

B
The aluminium sphere will experience more buoyant force than the iron sphere.

C
The iron sphere will experience more buoyant force than the aluminium sphere.

D
All the above statements are incorrect.

Solution

Buoyant force = Density of the liquid x Volume of the liquid displaced x Acceleration due to gravity
Greater is the density of the liquid, greater is the buoyant force. Water has more density as compared to alcohol and will exert more buoyant force as compared to the alcohol.
Question 15
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A force of 10 kg wt is applied on the head of a nail of area of cross-section (of the tip) 0.0001 cm². What is the pressure exerted?

A
10¹⁰ N m^-2

B
10⁶ N m^-2

C
10^-6 N m^-2

D
10^-10 N m^-2

Solution

Here, force = 10 kg wt = 100 N
Area = 0.0001 cm² = 10^-8m²Hence, pressure
Question 16
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When you press a rubber sucker against a surface, most of the air between its cup and the surface escapes out. To pull the rubber sucker off the surface, the applied force should be

A
equal to the atmospheric pressure

B
large enough to overcome the atmospheric pressure

C
less than the atmospheric pressure

D
None of the above

Solution

The rubber sucker sticks to the surface because the pressure of atmosphere acts on it. To pull the sucker off the surface, the applied force should be large enough to overcome the atmospheric pressure.
Question 17
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What happens when a stream of air is blown through a tube under one of the pans of a physical balance in equilibrium?

A
The pan will go up.

B
The pan will not be affected.

C
The pan will go down.

D
The pan will oscillate.

Solution

As the stream of air is blown through a tube under one of the pans, due to the high air speed, the pressure below the pan decreases as compared to the pressure above the pan. Hence, there will be a net downward force acting on the pan and the pan will go down.
Question 18
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A deep sea diver may hurt his eardrum during diving because of

A
lack of oxygen

B
high atmospheric pressure

C
high water pressure

D
All of the above

Solution

When a diver dives into the deep sea, there is water on the outside of the ear drum, but air on the inside. The pressure inside will still be equal to atmospheric pressure. However, on the outside, the pressure will be greater. This means that the pressure of air inside the ear will not cancel the pressure of the water outside. There will be net inward force due to this pressure difference, as a result of which the eardrum will stretch. This stretching of the eardrum hurts.
Question 19
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Water is flowing through a pipe under constant pressure. At some place, the pipe becomes narrow. The pressure of water at this place

A
increases

B
decreases

C
remains the same

D
depends on several factors

Solution

As the area of cross section decreases velocity increases. At the narrow end as the area of cross section decreases, velocity increases.
As the velocity increases, pressure decreases.
Question 20
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A raft is 2.35 m wide, 1.25 m long, and 0.365 m deep. What is the buoyant force on the raft, if only 0.125 m of the raft remains above water? (Take g = 10 m/s²)

A
10,500 N

B
3590 N

C
7050 N

D
6910 N

Solution

Upthrust acting on the object = Weight of the water displaced
Weight of the water displaced = Volume of water displaced (Volume of the object in the water) × Density × g
Volume of water displaced = 2.35 × 1.25 × 0.24 = 0.705 m³Hence, upthrust = 0.705 × 10³× 10 = 7050 N