Solved Examples of Archimedes’ Principle

Practice Problems on Archimedes’ Principle

Example 1: A body weighs 400 gf in air and 280 gf when completely immersed in water. Calculate: (1)the loss in weight of the body. (2) Calculate the volume of water displaced. (3) The upthrust on the body.

Solution:

Given: Weight of the object in air = 400 gf

Weight of the body in water = 280 gf

(1)Loss in weight in water = 400 gf – 280 gf = 120 gf

(2)Weight of water displaced = weight of object reduced = 120 gf

(3)Upthrust = loss of weight in water = 120 gf

Example 2: A piece of iron of density 7.8× 10³ kg m^-3 and volume 100cm³ is completely immersed in water(ρ = 1000kgm^-3). Calculate : (1) the weight of iron piece in air, (2) the upthrust and, (3) its apparent weight in water.(Take g = 10ms^-2)

Solution:

Given: Volume of iron piece = 100cm³= 10^-4m³

(1)Weight of iron piece in air = Volume × Density × g = 10^-4 × 7.8 × 10³ × 10 = 7.8N

(2) Upthrust = V_L× ρ × g = 10^-4 × 1000 × 10 = 1N

(3) Apparent weight = True weight – Upthrust =7.8N – 1N = 6.8N

Example 3: A metal sphere of radius 7cm³ and density 9gcm^-3 is suspended by a thread and is immersed completely in a liquid of density 3gcm^-3. Find: (1) the weight of the sphere, (2)the upthrust on the sphere and, (3) the tension on the thread.

Solution:

Given: radius of the sphere = 7cm³

volume_sphere = 4/3× π× r³ = 4/3× 22/7× 7× 7× 7 = 4312/3 = 1437.33 cm³

mass_sphere = V × D = 4312 / 3 × 9 = 12936

(1) weight = 12936 gf

(2) upthrust = weight of liquid displaced = V × D × g = 4312 / 3 × 3 × g = 4312 gf

(3) tension on the thread = total downward force = apparent weight of the sphere = original weight – upthrust = 12936 gf – 4312 gf = 8624 gf

Archimedes Principle

Archimedes Principle is a fundamental concept in fluid mechanics, credited to the ancient Greek mathematician and physicist Archimedes. According to Archimedes’ Principle, when an object is immersed in a fluid the object experiences an upward force whose magnitude is equal to the weight of the fluid displaced by the object.

Archimedes’ principle has applications in various fields, from ship design to understanding the behavior of objects in water. Archimedes’ Principle is important for class 9 students.

In this article, we are going to learn about what is Archimedes Principle, its formula, how to derive it, its application, and its experimental verification of Archimedes

Table of Content

What is Archimedes’ Principle?
Experimental Verification of Archimedes’ Principle
Archimedes’ Principle Formula
Applications of Archimedes’ Principle
Solved Examples

Solved Examples of Archimedes’ Principle

Archimedes Principle

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