Archimedes Principle Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. If the weight of the object is more than the weight of the water displaced, the object

1. Floats
2. Sinks
3. Remains constant
4. None of the above

Ans. The correct answer is b. Sinks

Explanation: According to the law of floatation, when the weight of the liquid displaced by immersed part of a body is equal to its weight, then a body starts floating. If the weight of the object is more than the weight of the liquid displaced, then the body sinks.

Ques. Who invented the Archimedes principle?

Ans. Archimedes, a Greek mathematician and physicist invented the Archimedes principle in the third century BC.

Ques. Density is given by the formula

1. Density = Mass – volume
2. Density = Mass × time
3. Density = Mass + volume
4. Density = Mass/volume

Ans. The correct answer is d. Density = Mass/volume

Explanation: The density of a substance is defined as the ratio of its mass per unit volume.

Ques. Archimedes’ principle helps to calculate the buoyancy of any floating object that is _____ immersed in a fluid

1. Completely
2. Only partially
3. Neither partially nor completely
4. Both partially and completely

Ans. The correct answer is d. Both partially and completely

Explanation: Archimedes' principle helps in calculating the buoyancy of any floating object immersed either completely or partially in a fluid.

Ques. Thrust force is given by the formula

1. ⍴ + V + g
2. ⍴ × V × g
3. ⍴ + V × g
4. ⍴ × V/g

Ans. The correct answer is b. ⍴ × V × g

Explanation: Thrust is a reaction force that can be measured using Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass causes that system to experience a force of the same magnitude but opposite direction. The formula of thrust force is given by ⍴ × V × g

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Short Answers Questions [2 Marks Questions]

Ques. State Archimedes Principle.

Ans. According to Archimedes' principle, when a body is submerged in a fluid, either partially or entirely, it experiences an upthrust or buoyant force equal to the weight of the displaced fluid by the body. Thus, 

Upthrust or buoyant force = weight of the fluid displaced by a body = weight of body the in the air - weight of body an in fluid.

Ques. Which is heavier cotton or iron Why?

Ans. The apparent weight of both is the same, but the buoyant force experienced by cotton is greater because the volume of cotton is greater than that of iron. As a result, the true weight of cotton is greater.

Ques. What is a hydrometer?

Ans. A hydrometer, sometimes known as a lactometer, is a device that measures the density or relative density of liquids using the idea of buoyancy. Typically, they are calibrated and graded with one or more scales, such as specific gravity.

Ques. Define relative density.

Ans. The ratio of the density of a substance (mass per unit volume) to the density of a certain reference material is known as its relative density or specific gravity. For gases, the reference is air at room temperature, whereas specific gravity measurements for liquids generally relate to water.

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Long Answers Questions [3 Marks Questions]

Ques. What are the applications of Archimedes' principle?

Ans. The followings are the application of Archimedes’ principle

• It helps in the design of ships and submarines. 
• Lactometers utilize it to test the purity of milk.
• It is used in hydrometers to determine fluid density.

Ques. A cylinder of height 30 cm and radius 7 cm is immersed completely in a fluid of density 1.3 x 10³ kg/m³. What is the buoyant force acting on it? (Take g = 10 m/s²)

Ans. The volume of the cylinder is given by

V_C = πr²h = 3.14 x (7 x 10^-2)² x (30 x 10^-2) = 4.62 x 10^-3 m³

Since the cylinder is completely immersed in the fluid, therefore

Buoyant force(F_B) = weight of the fluid displaced

⇒ F_B = density of fluid x volume of cylinder x g

⇒ F_B = 1.3 x 10³ x 4.62 x 10^-3 x 10 = 60 N

Ques. How can Archimedes’ principle be applied to ships?

Ans. Archimedes established the buoyancy principle, which states that a ship will continue to float if the weight of the water it displaces is equal to the ship's weight. As a result, anything will float if it has a shape that allows it to displace its own weight in water before it reaches the point of submerging.

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Very Long Answers Questions [5 Marks Questions]

Ques. A block of wood floats in water with one-third of its volume submerged. In oil, the block floats with two-thirds of its volume submerged. Find the density of (a) Wood (b) Oil, if the density of water is 10³ kg/m³

Ans. Let V₀ be the total volume of the block of wood.

We have

Density of body / Density of fluid = Volume of immersed part of the body / Total volume of body

Case (a): When the fluid is water, then the volume of immersed part of the wooden block is V₀/3. Therefore using the formula

Density of wood / Density of water = Volume of immersed part of the wooden block / Total volume of the wooden block

⇒ Density of wood / 10³ = (V₀/3) / V₀

⇒ Density of wood = 10³ / 3 = 333 kg/m³

Case (b): When the fluid is oil, then the volume of immersed part of the wooden block is 2V₀/3. Therefore using the formula

Density of wood / Density of oil = Volume of immersed part of the wooden block / Total volume of the wooden block

⇒ 333 / Density of oil = (2V₀/3) / V₀ = 2/3

⇒ Density of oil = 500 kg/m³

Ques. A body floats with 5/6 th of its total volume inside the water. When it floats in a liquid having a relative density of 1.2, what fraction of its volume is outside the liquid?

Ans. The relative density of a liquid is defined as the ratio of the density of the liquid to the density of water i.e.

Relative density = ρ_liquid / ρ_water

Let V₀ be the total volume of the block, then we have

Density of body / Density of fluid = Volume of immersed part of the body / Total volume of the body

When the body floats in water, then

Density of body(ρ_body) / Density of water(ρ_water) = (5V₀/6) / V0

⇒ ρ_body = 5ρ_water / 6 …(i)

Now, Let x be the volume of immersed part of the body when immersed in a liquid of density ρ_liquid then

ρ_body / ρ_liquid = xV₀/V₀ = x

⇒ ρ_body = xρ_liquid

Using equation (i)

5ρ_water / 6 = xρ_liquid

⇒ ρ_liquid / ρ_water = 5/6x

But ρ_liquid / ρ_water = 1.2 (given), therefore

1.2 = 5/6x

⇒ x = 25 / 36

Hence, x = 25/36 part of the volume of the body is immersed in liquid.

Therefore, the fraction of volume outside the liquid is equal to 1 - 25/36 = 11/36

Ques. A solid body floating in water has 1/5th of its volume immersed in it. What fraction of its volume will be immersed, if it floats in a liquid of specific gravity 1.2?

Ans. Specific gravity, also known as the relative density of a liquid is defined as the ratio of the density of the liquid to the density of water i.e.

Relative density = ρ_liquid / ρ_water = 1.2 (given)

Let V₀ be the total volume of the solid, then we have

When the body floats in water, then

Density of body(ρ_body) / Density of water(ρ_water) = (V₀/5) / V₀

⇒ ρ_body = ρ_water / 5 …(i)

Now, Let x be the volume of immersed part of the body when immersed in a liquid of density ρ_liquid then

ρ_body / ρ_liquid = xV₀/V₀ = x

⇒ ρ_body = xρ_liquid

Using equation (i)

ρ_water/ 5 = xρ_liquid

⇒ ρ_liquid / ρ_water = 1/5x

⇒ 1.2 = 1/5x

⇒ x = 1/6

Hence, x = 1/6 part of the volume of the body is immersed in liquid.

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