Archimedes' principle of buoyancy states that when a body is totally or partially immersed in a fluid, it is buoyed up by a force which equals to-
Weight of the fluid displaced by the body
Understanding Archimedes' Principle and Buoyancy
Archimedes' principle is a fundamental concept in physics that explains why objects float or sink in a fluid. It relates the buoyant force acting on an object to the fluid it displaces.
What is Archimedes' Principle?
Archimedes' principle states that when a body is submerged in a fluid, either partially or totally, it experiences an upward force. This upward force is known as the buoyant force.
The principle specifies the magnitude of this buoyant force:
The buoyant force is equal to the weight of the fluid displaced by the body.
Exploring the Buoyant Force Calculation
The weight of the displaced fluid can be calculated using the formula:
Weight = mass × acceleration due to gravity
The mass of the displaced fluid is its density multiplied by its volume:
mass = density of fluid × volume of displaced fluid
So, the buoyant force \(F_B\) can be expressed mathematically as:
\[F_B = \rho_{fluid} \cdot V_{displaced} \cdot g\]
Where:
- \(F_B\) is the buoyant force
- \(\rho_{fluid}\) is the density of the fluid
- \(V_{displaced}\) is the volume of the fluid displaced by the body (which is equal to the volume of the submerged part of the body)
- \(g\) is the acceleration due to gravity
This formula confirms that the buoyant force depends only on the properties of the fluid (\(\rho_{fluid}\), \(g\)) and the volume of the body submerged in it (\(V_{displaced}\)), which determines the volume of fluid displaced.
Analyzing the Options for Archimedes' Principle
Let's examine the given options based on our understanding of Archimedes' principle:
- Option 1: Difference of weights of the fluid displaced and that of the body
This option is incorrect. The buoyant force is directly equal to the weight of the fluid displaced, not the difference between that weight and the weight of the body. The relationship between buoyant force and the body's weight determines if it floats or sinks, but the buoyant force itself is defined by the displaced fluid. - Option 2: Weight of the body and fluid displaced by the body
This option is also incorrect. The buoyant force is not the sum of the weight of the body and the weight of the fluid displaced. It is solely the weight of the displaced fluid. - Option 3: Weight of the fluid displaced by the body
This option correctly states Archimedes' principle. The buoyant force is defined as being equal to the weight of the volume of fluid that the submerged part of the body pushes out of the way (displaces). - Option 4: Weight of the body
This option is incorrect. The weight of the body is the force pulling the body downwards due to gravity. The buoyant force is an upward force exerted by the fluid. While the weight of the body is crucial in determining if an object floats (when buoyant force equals body's weight), the buoyant force itself is not equal to the body's weight unless the object is floating.
Therefore, the statement that accurately describes the buoyant force according to Archimedes' principle is that it equals the weight of the fluid displaced by the body.
Revision Table: Key Concepts of Buoyancy
| Concept | Description |
|---|---|
| Buoyant Force (\(F_B\)) | The upward force exerted by a fluid on a submerged or partially submerged object. |
| Archimedes' Principle | States that the buoyant force equals the weight of the fluid displaced by the object. |
| Fluid Displaced | The volume of fluid pushed aside by the submerged part of an object. Its volume is equal to the submerged volume of the object. |
| Condition for Floating | When the buoyant force is equal to the weight of the object (\(F_B = W_{body}\)). This happens when the average density of the object is less than or equal to the density of the fluid. |
| Condition for Sinking | When the buoyant force is less than the weight of the object (\(F_B < W_{body}\)). This happens when the average density of the object is greater than the density of the fluid. |
Additional Information: Applications of Archimedes' Principle
Archimedes' principle is widely applicable and explains many everyday phenomena. Some examples include:
- Ships Floating: Even large, heavy ships made of steel can float because their hollow shape displaces a large volume of water. The weight of this displaced water equals the total weight of the ship, providing enough buoyant force.
- Submarines: Submarines use ballast tanks to control their buoyancy. By filling or emptying these tanks with water, they change their average density and thus the buoyant force, allowing them to dive or surface.
- Hot Air Balloons: Although the principle is usually discussed for liquids, it applies to any fluid, including air. A hot air balloon rises because the hot air inside is less dense than the surrounding cooler air. The buoyant force from the displaced cooler air is greater than the weight of the balloon and the hot air inside.
- Hydrometers: These devices are used to measure the specific gravity (or relative density) of liquids. They float higher in denser liquids and lower in less dense liquids, demonstrating Archimedes' principle.
Understanding Archimedes' principle helps us comprehend why certain objects float while others sink, and how this principle is used in various technologies.
Important Questions from Buoyancy and Floatation
Centre of buoyancy is -
According to Archimedes principle, the upward force experienced by a body immersed in a fluid is equal to which of the following?
- 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/m 3 . Then the weight of the block is
- Which of the following statement relating to the stability of floating and submerged bodies is incorrect?
A jar is filled with a liquid up to the mark of 1 litre and weighed. The weight of the liquid is found to be 5.5 N. The specific gravity of the liquid will be approximately
