Archimedes’ Principle MCQ Quiz - Objective Question with Answer for Archimedes’ Principle - Download Free PDF

Calculation:

The Upthrust force is equal to \(V\rho_{liquid} \left (g - a\right )\)

where, a = downward acceleration,

V = volume of liquid displaced

But for free fall a = g

\(\therefore\) Upthrust = 0

Solution:

When an ice cube floats in water, it displaces an amount of water equal to the weight of the ice cube. As the ice melts, it turns into water and occupies the volume that was previously displaced by the ice.

Ice is less dense than water, which is why it floats. The volume of water produced by the melting ice will be exactly equal to the volume of water that was displaced by the ice cube while it was floating.

Therefore, when the ice melts, the water level in the glass remains the same.

∴ The correct answer is option 3: Remains the same.

Calculation:

Mg = FB ⇒ (400 × 10^–3) = 10³ × V_d

V_d = 400 × 10^–6 m³

(Vol.)_outside = (10 × 10^–2)³ – 400 × 10^–6

= 600 × 10^–6 m² = 600 cm³ 

Calculation:

Given the body is half immersed in the water.

Let \(\rho\) be the density of water and \(m\) be the mass of the sphere initially.

\(\Rightarrow mg=\dfrac{V}{2}\rho g\)

Let \(V_0\) volume is added to the sphere. Then the weight of sphere \(=mg+V_0\rho g\)

After it is completely immersed:

Buoyancy force \(=V\rho g\)

Both the forces should be equal:

\(\Rightarrow mg+V_o\rho g=V\rho g\)

\(\Rightarrow V_0=\dfrac{V}{2}\)

The correct answer is Equal to its own volume.

Key Points

• Archimedes' Principle states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object.
• The principle applies to both floating and submerged objects.
• For a totally immersed object, the volume of the fluid displaced is equal to the volume of the object itself.
• This principle helps in determining the volume and density of objects.

Important Points

• Archimedes' Principle is fundamental in the field of fluid mechanics.
• This principle can be used to determine whether an object will float or sink in a fluid.
• It is also used in designing ships and submarines to ensure they remain buoyant.
• The principle is named after the ancient Greek mathematician and inventor Archimedes.

The correct answer is Hydrometer.

Key Points

• The hydrometer basically consists of a weighted, sealed, long-necked glass bulb immersed in the measured liquid, the flotation depth shows the liquid density, and the neck can be calibrated to read the actual gravity value.
• A hydrometer used for determining the density of liquids is based on Archimedes' principle.

Important Points

• Archimedes principle:
• It states that a body when wholly or partially immersed in liquid experiences an upward thrust which 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

CONCEPT:

• Archimedes' principle states that 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 and acts in the upward direction at the center of mass of the displaced fluid.

EXPLANATION:

• From the above definition, option 3 is correct.

• Laws of Floatation: The three conditions required for the body to float on water are:

1. The weight of the body in the figure is equal to the buoyant force. (c) (d)

2. The weight of the body is greater than the weight of the fluid displaced i.e. buoyant force.  (b)

3. The weight of the body is less than the weight of the fluid displaced i.e. buoyant force. (a)

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”.

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

\(\Rightarrow V = \frac{{0.7g}}{{ρ g}} = \frac{{0.7}}{{1000}} = 7 \times {10^{ - 4}}\;{m^3} = 700\;c{m^3}\)

Total volume of the cube = (10 cm) 3 = 1000 cm3

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:

F_b =  ρ × g × V

Where F_b 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.

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%

The correct answer is option 2.

Concept:​

• A floating object displaces an amount of water equal to its own weight. 
• Since water expands when it freezes, one unit (of weight) of frozen water has a larger volume than one unit of liquid water.

Explanation:

• As the density of oil water and ice is as follows:

d_ice = 0.91 g/cm³, d water = 1 g/cm³, d_oil is = 0.85 g/cm³

Since the density of ice is greater than that of kerosene, ice will not float in kerosene. Ice will actually sink in kerosene. Therefore, when ice is dropped into kerosene, it initially sinks to the bottom and displaces its volume in kerosene.

Sinking of ice in kerosene: The ice sinks to the bottom because the density of ice (0.91 g/cm³) is greater than the density of kerosene (0.85 g/cm³).
The volume of kerosene displaced by the ice is equal to the volume of the ice.
Melting of ice: When ice melts, it turns into liquid water.
Liquid water is denser than kerosene, so the water will also settle at the bottom.
 

While ice is solid and has sunk: The ice displaces an amount of kerosene equal to its own volume. The volume of kerosene displaced ((\( V_{displaced} )) is: [ V_{displaced} = \text{Volume of ice} \)]
When ice melts into water: The volume of water formed is not the same as the volume of ice (since mass and density relationships are preserved

d_ice = Mass /V_ice ;  mass = dice x Vice

dwater = Mass /V_water ;  mass = d_water x Vi_water

dice x Vice = dwater x Viwater
0.91 x Vice = 1 x Viwater

Volm of ice is grater then water so, when ice melt volm of water is less then that of ice and level of kerosene will fall.

So, the correct observation is that the level of kerosene oil will decrease.

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.

EXPLANATION:

• 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 F_B.

⇒ FB = Vdisplaced, ρg

⇒ FB = f(Vdisplaced, ρ)

So, the correct answer is option 3.

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 

Explanation:

Archimedes principle: It states that a body, when wholly or partially immersed in liquid, experiences an upward thrust which 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

Archimedes’ principle has many applications.

• It is used in designing ships and submarines. 
• Lactometers, which are used to determine the purity of a sample of milk, and hydrometers used for determining the density of liquids, are based on this principle.
• The hydrometer basically consists of a weighted, sealed, long-necked glass bulb immersed in the measured liquid; the flotation depth shows the liquid density, and the neck can be calibrated to read the actual gravity value.
• A barometer is a scientific instrument that is used to measure air pressure.