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All questions of Archimedes’ Principle and Law of Floatation for EmSAT Achieve Exam

A solid of density 900 kg/m3 floats in oil. The oil floats on water of density 1000 kg/m3 . The density of oil in kg/m3 could be.  
  • a)
    950
  • b)
    850
  • c)
    800
  • d)
    1050
Correct answer is option 'A'. Can you explain this answer?

Arien Instructors answered
  • If the solid with a density of 900 kg/m³ is able to float in the oil and the oil, in turn, floats on water with a density of 1000 kg/m³, then indeed the density of the oil must be between the densities of the solid and the water.
  • A solid of density 900 kg/m3 floats in oil as the density of solid is less than that of oil.
  • And the oil floats in water as its density is less than that of water.
  • So, the density of oil must be between 900 kg/m3 to1000 kg/m3.
  • Therefore, the density of oil could be 950 kg/m3.
  • This density would allow the solid to float in the oil, and the oil would float on the water.
Thus, A solid of density 900 kg/m3 floats in oil. The oil floats on water of density 1000 kg/m3. The density of oil in kg/m3 could be 950 kg/m3.
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The balls of iron and aluminium of same diameter are dipped in water. Which is the correct statement?
  • a)
    The upthrust on the iron ball will be more than the aluminium ball.
  • b)
    The upthrust on aluminium ball is more than the iron ball.
  • c)
    The upthrust on both balls will be the same.
  • d)
    More than one of the above.
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
The correct answer is The upthrust on both balls will be the same.
Key Points
  • The balls of iron and aluminium of the same diameter will have the same volume.
  • So, the buoyant force exerted by water on both the balls will be the same.
  • Buoyant Force is defined as the upward force exerted by a fluid on the immersed body. 
  • It is also called upthrust.
Additional Information
  • Archimedes’ principle states that when an object immersed in fluid experiences a buoyant force that is equal in magnitude to the force of gravity on the displaced fluid.
  • When an object is immersed wholly or partially in a fluid, then there is some apparent loss in its weight. This loss in weight is equal to the weight of the liquid displaced by the body.  

Consider the following statement 
Assertion: A human floats easily by using a rubber tube.
Reason: An inflated rubber tube has low weight and large volume and increases the upthrust.
  • a)
    Assertion is not correct, reason is correct and reason is not the correct explanation of assertion.
  • b)
    Assertion is correct, reason is correct and reason is the correct explanation of assertion.
  • c)
    Assertion is correct, reason is incorrect.
  • d)
    Assertion is incorrect, reason is correct.
Correct answer is option 'B'. Can you explain this answer?

Sara Al Nuaimi answered
Understanding the Assertion and Reason
The assertion states that a human floats easily by using a rubber tube, while the reason provides an explanation related to the properties of the rubber tube.
Assertion Explained
- The assertion is correct because a rubber tube, when inflated, increases buoyancy.
- When a person uses a rubber tube, it helps them stay afloat on water due to the principle of buoyancy.
Reason Explained
- The reason given is also correct. An inflated rubber tube has a low weight relative to its large volume.
- This large volume of air inside the tube displaces a significant amount of water, which increases the upward force (upthrust) acting on the tube and the person using it.
Connection Between Assertion and Reason
- The reason correctly explains why the assertion is true. The low weight and large volume of the inflated rubber tube are crucial for achieving buoyancy.
- The upthrust produced is what allows humans to float easily when using the tube.
Conclusion
- Both the assertion and the reason are correct.
- Importantly, the reason provided is a valid and accurate explanation of the assertion.
In summary, option 'B' is indeed the correct choice because both the assertion and the reason are true, and the reason effectively explains why the assertion holds true.

An object X sinks in liquids P and Q but floats in liquid R. Which of the following conclusions can be made from these observations?
A) Density of X is more than the density of P
B) Density of X is less than the density of R
C) Density of P is equal to the density of R
D) Density of P is less than the density of R
  • a)
    A, B, C
  • b)
    A, B, D
  • c)
    B, C, D
  • d)
    A, C, D
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
Concept:
Archimedes principle:
  •  It states that a body, when wholly or partially immersed in liquid, experiences an upward thrust that is equal to the volume of the liquid.
  • Archimedes Principle is also known as the physical law of buoyancy.
  • When a solid is fully immersed in a liquid, it loses weight, which is equal to the weight of the liquid it displaces.
Apparent weight= actual weight−buoyant force= mg−ρgV
Where m = mass of the object and ρ = density of the fluid
 
 Buoyant force:
  • ​When a body is wholly or partially immersed in a fluid at rest, the fluid exerts pressure on the surface of the body in contact with the fluid.
  • The pressure is greater on lower surfaces of the body than on the upper surfaces as the pressure in a fluid increases with depth.
  • The resultant of all the forces is an upward force called buoyant force
Explanation:
Law of Floatation:
  • When an object is placed on liquid, an upthrust acts on it.
  • This upthrust is more than weight when the density of the object is less than weight. The object floats in this case.
  • If the density of the object is more, the object will sink as the weight will be more than upthrust.
  • When a body is immersed partially or completely in a fluid (liquid or gas), it experiences an upthrust or buoyant force that is equal to the weight of the fluid displaced by the body.
  • Considering, the question statement:
    • ρR > ρX > ρP
So, from the above relation options A, B, and D are the correct ones.

What percent of the total volume of an iceberg floats above the water surface? Assume the density of ice to be 920 kg/m3 and the density of water to be 1000 kg/m3 .
  • a)
    6
  • b)
    8
  • c)
    92
  • d)
    20
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
Concept:
When a body is either wholly or partially immersed in a fluid, a lift is generated due to the net vertical component of hydrostatic pressure forces experienced by the body. This lift is called the buoyant force and the phenomenon is called buoyancy.
The Archimedes principle states that the buoyant force on a submerged body is equal to the weight of the liquid displaced by the body and acts vertically upward through the centroid of the displaced volume.
Thus, the net weight of the submerged body, (the net vertical downward force experienced by it) is reduced from its actual weight by an amount that equals the buoyant force.
FB = ρghA = ρgV
Weight of cube = buoyancy force
ρiceViceg = ρwVVDg
Calculation:
Given:
ρice = 920 kg/m3, ρw =1000 kg/m3
Let the x be the volume of iceberg floats above the water surface.
ρiceVg = ρwg(V - x)
920 × V × g = 1000 × g × (V - x)
0.92V = (V - x)
x = 8%

A piece of ice is dropped in a vessel containing kerosene oil. When ice melts, the level of kerosene oil will
  • a)
    rise
  • b)
    fall
  • c)
    remain same
  • d)
    More than one of the above
Correct answer is option 'A'. Can you explain this answer?

Layla Al Hashemi answered
Understanding the Scenario
When a piece of ice is dropped into a vessel containing kerosene oil, we need to analyze what happens when the ice melts. Ice is less dense than water, and when it melts, it converts into water, which is denser than both ice and kerosene oil.
Ice in Kerosene Oil
- Ice floats on kerosene oil because it is less dense than kerosene.
- When the ice is submerged, it displaces a volume of kerosene oil equal to the weight of the ice.
Melting Process
- As the ice melts, it turns into liquid water.
- The volume of water produced from the melted ice will be less than the volume of kerosene oil displaced when the ice was floating.
Effect on Kerosene Oil Level
- Since the volume of the water formed from the melted ice is less than the volume of kerosene oil that was displaced by the floating ice, the overall volume of kerosene oil displaced decreases.
- Therefore, as the ice melts, the kerosene oil level rises.
Conclusion
- The correct answer is option 'A': The level of kerosene oil will rise when the ice melts.
This phenomenon can be attributed to the differences in density between ice, water, and kerosene oil, illustrating important principles of buoyancy and displacement.

On which of the following factors the magnitude of the buoyant force acting on a body in a given fluid depends?
  • a)
    Weight of the body immersed in it.
  • b)
    Shape of the body immersed in the fluid.
  • c)
    Density of the fluid and mass of the body immerse in it.
  • d)
    Density of the fluid and the volume of the body immersed in it.
Correct answer is option 'D'. Can you explain this answer?

Arien Instructors answered
ey Points
  • The buoyant force depends on the volume of the liquid displaced. The buoyant force depends on the mass of the object, the weight of the object, and its density.
  • The buoyant force depends directly upon:
    • The volume of the fluid displaced.
    • The density of the fluid in which the body is immersed.
    • Acceleration due to gravity at the place.
Important Points
  • The three types of buoyancy are positive buoyancy, negative buoyancy, and neutral buoyancy.
    • Positive buoyancy is when the immersed object is lighter than the fluid displaced and this is the reason why the object floats.
    • Negative buoyancy is when the immersed object is denser than the fluid displaced which results in the sinking of the object.
    • Neutral buoyancy takes place when the weight of an immersed object is equal to the fluid displaced. 

A balloon moving up in the air is based on the-
  • a)
    Pascal law
  • b)
    Archimedes principle
  • c)
    Bernoulli’s Equation
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
CONCEPT:
  • A simple device that uses hot air or light gas to move up in the air is called a balloon.
  • Archimedes principle: Any object which is floating in a fluid is acted upon by an upward force whose magnitude is equal to the weight of the fluid displaced.
    • The balloon is based on the principle of Archimedes.
EXPLANATION:
  • When the air is being heated the density of that air gets reduced compared to the density of surrounding air or we can use the gas having less density than that of air.
  • Due to the difference in density, the balloon lifted above the ground and moves up in the air.
  • Thus a balloon is based on the Archimedes principle. So option 2 is correct.
EXTRA POINTS:
  • Bernoulli's principle: For a streamlined flow of an ideal liquid in a varying cross-section tube the total energy per unit volume remains constant throughout the fluid.
  • Pascal’s principle: Pascal’s Law is the principle of transmission of fluid-pressure.
    • It says that "a pressure exerted anywhere in a point of the confined fluid is transmitted equally in all directions throughout the fluid”.

When the weight of the fluid displaced is less than the weight of the solid body then:
  • a)
    Body floats
  • b)
    The body will be half immersed in the fluid
  • c)
    The body sinks in a fluid
  • d)
    The body will be rotating
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
Archimedes principle: 
  • It is used to explain the law of flotation or upward thrust experienced when immersed in a fluid. 
  • The principle of Archimedes states “When a body is immersed in a liquid, an upward thrust, equal to the weight of the liquid displaced, acts on it.”
  • The flotation and sinking of an object are dependent upon the relative density with each other.
    • If the density of the object is more than the density of the liquid, the object will sink.
    • On the other side, if the density of an object is less than the liquid, then it will float over it.
    • If the density of the object and liquid is equal to each other, they are in equilibrium and float and sink both at the same time
    • Therefore, the sinking or floating of an object depends on the difference in density of objects and liquid.
Weight = m × g = ρ × g × V
  • If the upthrust force (equal to weight) exerted on the body by the fluid is greater than the weight of the body, then the body floats. While, if upthrust is lesser, then the body sinks.

A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:
  • a)
    0.178 m
  • b)
    0.250 m
  • c)
    0.403 m
  • d)
    0.500 m
Correct answer is option 'C'. Can you explain this answer?

Rasha Khalifa Al Gurg answered
Given data:
- Density of water = 1000 kg/m³
- Specific gravity of wooden plank = 0.5
- Load on the plank = 1.5 kN
- Dimensions of the plank: 1 m × 1 m × 0.5 m

Calculating the weight of the plank:
- Weight of the plank = Volume × Density × Specific gravity of wood
- Volume = 1 m × 1 m × 0.5 m = 0.5 m³
- Weight of the plank = 0.5 m³ × 1000 kg/m³ × 0.5 = 250 kg = 2.5 kN

Calculating the buoyant force acting on the plank:
- Buoyant force = Weight of water displaced = Weight of water × Volume displaced
- Weight of water displaced = Load on the plank + Weight of the plank
- Weight of water displaced = 1.5 kN + 2.5 kN = 4 kN
- Buoyant force = 4 kN
- Buoyant force = Weight of water × Volume displaced
- 4 kN = 1000 kg/m³ × 9.81 m/s² × Volume displaced
- Volume displaced = 0.407 m³

Calculating the depth of the plank below the water surface:
- Area of the plank in contact with water = 1 m × 1 m = 1 m²
- Volume displaced = Area of contact × Depth below water surface
- Depth below water surface = Volume displaced / Area of contact
- Depth below water surface = 0.407 m³ / 1 m² = 0.407 m ≈ 0.403 m
Therefore, the depth of the plank lying below the water surface is approximately 0.403 meters. So, the correct answer is option 'C'.

What is the specific gravity of a marble stone, which weighs 400 N in air, and 200 N in the water? (g = 10m/s2)
  • a)
    8
  • b)
    6
  • c)
    4
  • d)
    2
Correct answer is option 'D'. Can you explain this answer?

Obaid Al Sharqi answered
Calculation of Specific Gravity:
To calculate the specific gravity of the marble stone, we can use the formula:
Specific Gravity = Weight in air / (Weight in air - Weight in water)
Given:
Weight in air = 400 N
Weight in water = 200 N
Acceleration due to gravity (g) = 10 m/s^2

Calculation:
Specific Gravity = 400 / (400 - 200)
Specific Gravity = 400 / 200
Specific Gravity = 2
Therefore, the specific gravity of the marble stone is 2.
Therefore, the correct answer is option D.

What happens to the buoyant force acting on an object when it is partially submerged in a fluid?
  • a)
    The buoyant force increases.
  • b)
    The buoyant force decreases.
  • c)
    The buoyant force remains the same.
  • d)
    The buoyant force is zero.
Correct answer is option 'C'. Can you explain this answer?

Aaditya Choudhury answered
Understanding Buoyant Force
The buoyant force is the upward force exerted by a fluid on a submerged or partially submerged object. This force is crucial in determining whether an object sinks, floats, or remains suspended in the fluid.
Principle of Buoyancy
According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid displaced by the object. This principle is applicable regardless of how much of the object is submerged.
Effect of Partial Submersion
- When an object is partially submerged, it displaces a volume of fluid equal to the submerged portion of the object.
- The buoyant force remains constant as long as the submerged volume and the density of the fluid do not change.
Key Points
- Buoyant Force is Constant: The buoyant force acting on a partially submerged object does not change with the amount of submersion as long as the displaced fluid volume remains the same.
- Weight of Displaced Fluid: The force is solely dependent on the weight of the fluid that the object displaces, not on the total volume of the object.
- Equilibrium: An object floats when the buoyant force equals the weight of the object. If the object is partially submerged, this balance indicates that the buoyant force remains equal to the weight of the displaced fluid.
Conclusion
Thus, when an object is partially submerged in a fluid, the buoyant force acting on it remains the same, confirming that the correct answer to the question is option 'C'.

A wooden block weighs 10 N in air and 6 N in water when fuly immersed.. What is the buoyant force acting on the block?
  • a)
    4 N
  • b)
    6 N
  • c)
    10 N
  • d)
    16 N
Correct answer is option 'B'. Can you explain this answer?

Mira Dey answered
Understanding Buoyant Force
The buoyant force is the upward force exerted by a fluid on an object that is fully or partially immersed in it. This force is responsible for making objects feel lighter in water compared to their weight in air.
Given Data
- Weight of the wooden block in air: 10 N
- Weight of the wooden block in water: 6 N
Calculating the Buoyant Force
To find the buoyant force acting on the block, we can use the following relationship:
- Buoyant Force = Weight in air - Weight in water
Let's calculate it:
- Weight in air = 10 N
- Weight in water = 6 N
- Buoyant Force = 10 N - 6 N
Result of the Calculation
- Buoyant Force = 4 N
Conclusion
The buoyant force acting on the block is 4 N.
Correct Answer
The options provided were:
- a) 4 N
- b) 6 N
- c) 10 N
- d) 16 N
The correct answer is option 'A', not 'B'.
Reasoning Behind the Choice
- The block weighs less in water due to the upward buoyant force acting against gravity.
- The difference in weight (10 N - 6 N) indicates the buoyant force, which is indeed 4 N.
In summary, the buoyant force is the reason the block appears lighter in water, and it is calculated by the difference in weight between air and water.

An object is put one by one in three liquids P, Q, and R having different densities. Consider the following statements and arrange the liquids in ascending order of densities.
(A) In liquid P, the object is completely submerged
(B) In liquid Q, objects float with (1/4)th part of their volume inside the liquid
(C) In liquid R, objects float with (1/2)th of their volume inside the liquid
  • a)
    R < Q < P
  • b)
    P < Q < R
  • c)
    Q < R < P
  • d)
    P < R < Q
Correct answer is option 'D'. Can you explain this answer?

Reem Al Saadi answered
Understanding Liquid Densities
To determine the order of densities of liquids P, Q, and R based on the behavior of objects placed in them, we analyze each statement provided.
Analysis of Liquids
- Liquid P:
- The object is completely submerged.
- This indicates that the density of liquid P is greater than the density of the object.
- Liquid Q:
- Objects float with (1/4)th of their volume submerged.
- According to Archimedes' principle, this means that the density of liquid Q is less than the density of the object but greater than (1/4)th of the object’s density.
- Liquid R:
- Objects float with (1/2)th of their volume submerged.
- This indicates that the density of liquid R is less than the density of the object but greater than (1/2)th of the object’s density.
Comparative Densities
From the above analyses, we can summarize:
- Density Relationships:
- Density of R < density="" of="" q="" />< density="" of="" />
Conclusion
Thus, we can arrange the liquids in ascending order of densities as follows:
- Ascending Order of Densities:
- R < q="" />< />
Therefore, the correct answer is option 'D': P < r="" />< q.="" this="" arrangement="" reflects="" that="" liquid="" r="" is="" the="" least="" dense,="" followed="" by="" liquid="" q,="" and="" finally="" liquid="" p="" has="" the="" highest="" density.="" q.="" this="" arrangement="" reflects="" that="" liquid="" r="" is="" the="" least="" dense,="" followed="" by="" liquid="" q,="" and="" finally="" liquid="" p="" has="" the="" highest="" />

A vertical gate closes a horizontal tunnel 4 m high and 4 m wide running full with water. The pressure at the bottom of the gate is 196.2 kN/m2. What will be the location of center of pressure? [ρ = 1000 kg/m3 , g = 9.81 m/s2]
  • a)
    5/27 m below the centroid of gate
  • b)
    2/27 m below the centroid of gate
  • c)
    1/27 m below the centroid of gate
  • d)
    4/27 m below the centroid of gate
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
Concept:
Pressure intensity is given as, P = ρgh
The height of the imaginary free surface of the water above the bottom of the gate equivalent to a pressure intensity of 196.2 kN/m2 is, 
The total pressure on gate is, P = wAx̅ 
Where, A = area of gate, x̅ = vertical distance of CG from free surface 
Vertical distance of CP from free surface is,
Where, IG = MOI at the center of axis, 
Calculation: 
Given:
ρ = 1000 kg/m3, g = 9.81 m/s2, A = 4 × 4, θ = 90°, P = 196.2 kN/m2. 
The height of the imaginary free surface of the water,
The total pressure on gate is, P = wAx̅ 
Vertical distance of CG from free surface, x̅ = 20 - 2 = 18 m
Vertical distance of CP from free surface is, 
The location of center of pressure below the centroid of gate is, 
y = h - x̅ 

A rectangular block 2 m long, 1 m wide and 1 m deep floats in water. The depth of immersion is 0.5 m. If water weighs 10 kN/m3. Then the weight of the block is
  • a)
    5 kN
  • b)
    20 kN
  • c)
    15 kN
  • d)
    10 kN
Correct answer is option 'D'. Can you explain this answer?

Arien Instructors answered
Concept:
When the density of the body is less than that of the water, it floats. According to Archimedes' principle the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
For floating bodies, the weight of the body = buoyancy force
Weight of the body = Immersed volume x Unit weight of water.
Calculations:
Given, 
L = 2m, B = 1 m, h = 1 m, γ = 10 kN/m3, d = 0.5 m
Weight of body = Buoyancy Force
Buoyancy (B) = Immersed volume × Unit weight of water
W = L x B x d × γ 
W = 2 x 1 x 0.5 × 10 = 10 kN 

When a floating ice cube melts, the volume of water
  • a)
    is less than the volume of the ice cube
  • b)
    is greater than the volume of the ice cube
  • c)
    is equal to the volume of the ice cube
  • d)
    none of the above
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
CONCEPT:
  • Archimedes' principle: A body at rest in a fluid is acted upon by a force pushing it upward called the buoyant force, which is equal to the weight of the fluid that the body displaces.
​The buoyant force (FB) is given by,
FB = ρfluid × g × Vobject
​EXPLANATION:
The floating ice will displace some volume of the water.
From Archimedes' principle, FB = ρwater × g × Vice      ----(1)
Weight of the displaced fluid (water) = mg = ρwater × Vdispalced water × g      ----(2)
For an object to stay afloat, the forces acting on it must be balanced ⇒ (1) = (2)
ρwater × g × Vice = ρwater × Vwater × g 
⇒  Vice = Vdispalced water
  • Therefore, when the ice melts, there will be no change in the water level as the melted ice will occupy the same volume as that of displaced water.

Which of the following statements is true regarding the stability of a submerged object?
  • a)
    An object is more stable when its center of gravity is above its center of buoyancy.
  • b)
    An object is more stable when its center of gravity is below its center of buoyancy.
  • c)
    An object's stability is not affected by the relationship between the center of gravity and the center of buoyancy.
  • d)
    An object's stability depends on the density of the fluid it is submerged in.
Correct answer is option 'B'. Can you explain this answer?

Paradigm Institute answered
Similar to a floating object, the stability of a submerged object is increased when its center of gravity is below its center of buoyancy. This ensures that any tilting or disturbance will create a restoring torque, bringing the object back to equilibrium.

A ship floats in water because:
  • a)
    The weight of the ship is greater than the buoyant force.
  • b)
    The weight of the ship is less than the buoyant force.
  • c)
    The weight of the ship is equal to the buoyant force.
  • d)
    The weight of the ship is not related to the buoyant force.
Correct answer is option 'B'. Can you explain this answer?

Paradigm Institute answered
According to Archimedes' principle, an object floats when the buoyant force acting on it is equal to or greater than its weight. In the case of a ship, the weight of the ship is less than the buoyant force exerted by the water, allowing it to float.

How does temperature affect the density of most substances?
  • a)
    No effect on density
  • b)
    Decreases density when heated
  • c)
    Makes density uniform
  • d)
    Increases density when heated
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
Temperature generally affects the density of most substances by decreasing their density when heated. As substances expand upon heating, their mass remains constant while their volume increases, leading to a lower density. This principle is important in various scientific and engineering applications, including thermodynamics and fluid mechanics.

Which fluid property allows a person to float more easily in the Dead Sea compared to a regular lake?
  • a)
    Temperature
  • b)
    Viscosity
  • c)
    Surface tension
  • d)
    Density
Correct answer is option 'D'. Can you explain this answer?

Arien Instructors answered
The property that allows a person to float more easily in the Dead Sea compared to a regular lake is the density of the fluid. The Dead Sea has a much higher salt concentration, increasing its density. This greater buoyancy makes it easier for individuals to float, as the buoyant force exceeds their weight more significantly than in less dense water.

Which of the following statements is true when an object is floating in equilibrium?
  • a)
    Buoyant force acts downward
  • b)
    Buoyant force is less than the weight of the object
  • c)
    Buoyant force equals the weight of the object
  • d)
    Buoyant force is greater than the weight of the object
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
When an object is floating in equilibrium, the buoyant force acting on it equals the weight of the object. This balance of forces allows the object to float without rising or sinking. This principle is a key aspect of Archimedes' principle and is fundamental in fluid dynamics.

In which scenario would an object sink in water?
  • a)
    When its weight is greater than the buoyant force
  • b)
    When its weight is less than the buoyant force
  • c)
    When it is fully submerged
  • d)
    When its weight is equal to the buoyant force
Correct answer is option 'A'. Can you explain this answer?

Arien Instructors answered
An object will sink in water when its weight is greater than the buoyant force acting on it. This situation occurs because the upward force of buoyancy cannot counteract the downward gravitational force, resulting in the object sinking. This principle can be observed with denser materials that displace less water relative to their weight.

A 700 gm solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? The density of the water 1000 kgm-3
  • a)
    300 cm3
  • b)
    100 cm3
  • c)
    400 cm3
  • d)
    200 cm3
Correct answer is option 'A'. Can you explain this answer?

Arien Instructors answered
Concept:
Archimedes Principle: When a body is fully or partially dipped in fluid, the fluid exerts a contact force on the body. The resultant of this contact force is known as buoyancy or buoyant force.
  • This force acts vertically upwards (opposite to the weight of the body).
  • Mathematically, F = Vρg [where, V = volume of liquid displaced, ρ = density of the liquid, g = acceleration due to gravity.]
  • A body floats on a fluid if the average density of the body is less than that of fluid.
  • The weight of the liquid displaced by the immersed part of the body must be equal to the weight of the body.
Calculation:
Given:
m = 700 g = 0.7 kg, a = 10 cm 
In floating bodies,
Weight of fluid = Buoyant force
Buoyant force = weight of water displaced. If V is the volume of cube inside the water, then the weight of water displaced = Vρg.
⇒ Vρg = 0.7 g
Total volume of the cube = (10 cm) 3 = 1000 cm3
∴ Volume outside the water = 1000 – 700 = 300 cm3

The ability of an object to float in a fluid depends on:
  • a)
    The object's mass.
  • b)
    The object's volume.
  • c)
    The object's shape.
  • d)
    All of the above.
Correct answer is option 'D'. Can you explain this answer?

Paradigm Institute answered
The ability of an object to float in a fluid depends on various factors, including its mass, volume, and shape. All of these factors affect theobject's buoyancy and determine whether it will float or sink.

When a cork floats in water with two-thirds of its volume submerged, what does this indicate about the buoyant force and the weight of the cork?
  • a)
    Buoyant force equals the weight of the cork
  • b)
    The cork is in a state of free fall
  • c)
    Buoyant force is greater than the weight of the cork
  • d)
    Buoyant force is less than the weight of the cork
Correct answer is option 'A'. Can you explain this answer?

Arien Instructors answered
When a cork floats with two-thirds of its volume submerged, it indicates that the buoyant force equals the weight of the cork. This balance allows the cork to float in equilibrium, demonstrating the principle of floatation where the weight of the fluid displaced by the submerged part of the cork is equal to the weight of the cork itself.

What causes the net upward force (upthrust) on a submerged object?
  • a)
    Pressure difference between the top and bottom surfaces
  • b)
    Weight of the object
  • c)
    Surface tension of the fluid
  • d)
    The shape of the object
Correct answer is option 'A'. Can you explain this answer?

Arien Instructors answered
The net upward force (upthrust) on a submerged object is caused by the pressure difference between the top and bottom surfaces of the object. The pressure at the deeper surface of the object is greater than that at the shallower surface, resulting in a net upward force that acts to lift the object.

What is the relationship between the volume of a submerged part of an object and the density of the fluid in which it is floating?
  • a)
    Inversely proportional
  • b)
    No relationship
  • c)
    Equal to its weight
  • d)
    Directly proportional
Correct answer is option 'A'. Can you explain this answer?

Arien Instructors answered
The relationship between the volume of the submerged part of an object and the density of the fluid in which it is floating is directly proportional. The more dense the fluid, the smaller the volume of fluid that needs to be displaced to support the object's weight, which is crucial in understanding floatation principles.

The upward force exerted by the liquid displaced by the body when it is placed inside the liquid is called
  • a)
    Centripetal Force
  • b)
    Force of Friction
  • c)
    Gravitational Force
  • d)
    Buoyant Force
Correct answer is option 'D'. Can you explain this answer?

Arien Instructors answered
CONCEPT:
  • Archimedes Principle: The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced fluid.
    • The value of thrust force is given by the Archimedes law which was discovered by Archimedes of Syracuse of Greece. When an object is partially or fully immersed in a liquid displaced by it.
    • Archimedes' principle tells us that this loss of weight is equal to the weight of liquid the object displaces. If the object has a volume of V, then it displaces a volume V of the liquid when it is fully submerged. If only a part of the volume is submerged, the object can only displace that much liquid.
  • Archimedes Principle Formula: In simple form, the Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as:
Fb =  ρ × g × V
Where Fb is the buoyant force, ρ is the density of the fluid, V is the submerged volume, and g is the acceleration due to gravity
​EXPLANATION:
  • When a body partially and fully emerged in any fluid it experiences an upward force that is equal to the weight of the fluid displaced by it and it is called buoyant force.
  • Hence option 4 is the correct answer.

A piece of brass (alloy of copper and zinc) weighs 12.9 g in air. When completely immersed in water weighs 11.3 g. what is the mass of copper contained in the alloy? Specific gravities of copper and zinc are 8.9 and 7.1 respectively.
  • a)
    6.7 gm
  • b)
    7.6 gm
  • c)
    4.6 gm
  • d)
    5.6 gm
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
Concept:
  • The Specific gravity of a substance is the ratio of its density to the density of water.
  • A substance with a specific gravity of less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a specific gravity greater than 1 will sink.
  • Whereas the relative density of a substance is defined as the ratio of densities of any two-sample, it can be expressed as
  • Archimedes' principle states that when a body immersed in a fluid, whether fully or partially submerged, the upward buoyant force that is exerted on it, is equal to the weight of the fluid that the body displaces.
  • Buoyant force: When an object is submerged in fluid fully or partially, an upward force is exerted on the body. This force is known as the buoyant force. 
Calculation:
Given:
Mass of water displaced = 12.9 - 11.3 = 1.6 g
⇒ Volume of water displaced = mass / density = 1.6/1 = 1.6 cm3
We know that,
Relative density = density of substance / density of water
Since density of water = 1 g/cm3
⇒ Density of copper = 8.9 g/cm3
Let the mass of copper in 12.9 gram of alloy is x
Volume of water displaced by the copper  = x/8.9 cm3
Similarly,
⇒ Density of zinc = 7.1 g/cm3
Also, the mass of zinc in alloy = 12.9 - x
Volume of water displaced by zinc = (12.9- x)/7.1 cm3
Hence total water displaced by the alloy,
Solving we get,
x = 7.614 gm.
Hence the mass of copper in the alloy is 7.614 gm.

What determines the amount of buoyant force acting on an object submerged in a fluid?
  • a)
    The fluid's viscosity
  • b)
    The volume of fluid displaced
  • c)
    The temperature of the fluid
  • d)
    The object's mass
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
The amount of buoyant force acting on an object submerged in a fluid is determined by the volume of fluid displaced by the object. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced, which depends directly on the submerged volume of the object.

What is the relationship between the density of an object and its ability to float in a fluid?
  • a)
    Only the shape of the object determines floatation
  • b)
    The greater the density, the easier it floats
  • c)
    The lesser the density, the easier it floats
  • d)
    Density has no effect on floatation
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
The relationship between density and floatation is such that the lesser the density of an object compared to the fluid, the easier it floats. If an object's density is less than that of the fluid, it will displace enough fluid to generate a buoyant force that can support its weight, allowing it to float.

Which of the following conditions must be met for an object to float?
  • a)
    The weight must be greater than the buoyant force
  • b)
    The weight must be equal to the buoyant force
  • c)
    The object must be fully submerged
  • d)
    The weight must be less than the buoyant force
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
For an object to float, the weight of the object must be equal to the buoyant force acting on it. This balance allows the object to maintain its position in the fluid without sinking or rising, adhering to the principle of floatation.

If a solid object has a density greater than that of water, what will happen to it when placed in water?
  • a)
    It will remain suspended
  • b)
    It will float
  • c)
    It will sink
  • d)
    It will dissolve
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
A solid object with a density greater than that of water will sink when placed in water. This is because the weight of the object exceeds the buoyant force provided by the displaced water, leading to a net downward force. This principle is commonly observed with metals and other dense materials.

What happens to the apparent weight of an object when it is submerged in a fluid?
  • a)
    It increases
  • b)
    It remains the same
  • c)
    It decreases
  • d)
    It becomes negative
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
The apparent weight of an object decreases when it is submerged in a fluid due to the upthrust acting on it. The buoyant force reduces the effective weight of the object, making it feel lighter in water than in air. This concept is crucial for understanding why objects can be more easily lifted in water.

Which property of a fluid affects the upthrust experienced by an object submerged in it?
  • a)
    Surface tension
  • b)
    Temperature
  • c)
    Viscosity
  • d)
    Density
Correct answer is option 'D'. Can you explain this answer?

Arien Instructors answered
The upthrust experienced by an object submerged in a fluid is affected by the fluid's density. A denser fluid exerts a greater buoyant force on the object, increasing the upthrust. This principle is essential in applications such as designing submarines and understanding how various objects behave in different fluids.

According to the law of floatation, when an object is immersed in a fluid, it displaces a volume of fluid equal to its own volume. This is known as:
  • a)
    Archimedes' principle
  • b)
    Pascal's law
  • c)
    Buoyant force
  • d)
    Principle of displacement
Correct answer is option 'D'. Can you explain this answer?

KS Coaching Center answered
The principle of displacement states that when an object is immersed in a fluid, it displaces a volume of fluid equal to its own volume. This principle is a fundamental concept related to Archimedes' principle.

The principle of floatation can be used to determine the ______ of an object.
  • a)
    Volume
  • b)
    Density
  • c)
    Weight
  • d)
    Pressure
Correct answer is option 'B'. Can you explain this answer?

Paradigm Institute answered
The principle of floatation can be used to determine the density of an object. By measuring the weight of the object in air and in a fluid, and knowing the density of the fluid, the density of the object can be calculated.

The pressure at any point in a fluid at rest is transmitted ______.
  • a)
    Equally in all directions.
  • b)
    Only in the upward direction.
  • c)
    Only in the downward direction.
  • d)
    In the direction of the fluid flow.
Correct answer is option 'A'. Can you explain this answer?

KS Coaching Center answered
According to Pascal's law, the pressure in a fluid at rest is transmitted equally in all directions. This is why, for example, when you squeeze a closed container filled with fluid, the pressure is distributed uniformly throughout the fluid.

The principle of floatation is based on the law of:
  • a)
    Conservation of mass.
  • b)
    Conservation of energy.
  • c)
    Conservation of momentum.
  • d)
    Conservation of volume.
Correct answer is option 'D'. Can you explain this answer?

Paradigm Institute answered
The principle of floatation is not directly related to the conservation of mass, energy, or momentum. It is based on the law of conservation of volume, which states that the volume of fluid displaced by an object is equal to the volume of the object.

What happens to the buoyant force when a submerged object is pushed deeper into the fluid?
  • a)
    It decreases
  • b)
    It increases
  • c)
    It disappears
  • d)
    It remains constant
Correct answer is option 'B'. Can you explain this answer?

Arien Instructors answered
When a submerged object is pushed deeper into a fluid, the buoyant force increases. This is due to the increase in pressure at greater depths, which results in a greater upward force acting on the submerged object. This principle is essential for understanding why certain objects float or sink depending on their depth in the fluid.

Which statement best describes the center of buoyancy for a submerged object?
  • a)
    Always above the center of gravity
  • b)
    Coincides with the center of gravity for all objects
  • c)
    Always below the center of gravity
  • d)
    Changes with the object's orientation
Correct answer is option 'C'. Can you explain this answer?

Arien Instructors answered
The center of buoyancy for a submerged object is always located above the center of gravity for a floating object. This positioning contributes to the stability of the object in the fluid. If the center of buoyancy is below the center of gravity, it helps maintain equilibrium and prevents the object from tipping over.

Chapter doubts & questions for Archimedes’ Principle and Law of Floatation - Physics for EmSAT Achieve 2025 is part of EmSAT Achieve exam preparation. The chapters have been prepared according to the EmSAT Achieve exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for EmSAT Achieve 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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