What Factors Affect the Upthrust Acting on an Object?
Understanding the concept of Upthrust And Law Of Floatation is crucial for JEE aspirants, as these principles explain why objects float or sink in fluids. Mastery of this topic ensures clarity on related questions in exams.
What is an Upthrust?
Whenever we try to submerge an object in water, we notice a resistance pushing it upwards. This resistance is known as upthrust or buoyant force. It acts upwards from the fluid on the object.
When an object is immersed, either partially or completely, the fluid exerts an upward force on it. This upward force is called upthrust, commonly denoted as FB, measured in Newtons (N) or kilogram-force (kgf).
Definition of Buoyancy
Buoyancy is the property of fluids to exert an upthrust on objects placed in them. Both liquids and gases can provide this effect, resulting in a feeling of lightness or even causing objects to rise.
- An object floats if its weight is less than the upthrust from the fluid.
- An object sinks if its weight is more than the upthrust of the fluid.
- Balloons filled with hydrogen rise due to buoyancy in air.
- Swimmers feel lighter because of water’s upthrust.
Archimedes’ Principle
Archimedes’ principle states: “A body partly or fully immersed in a fluid experiences an upward force equal to the weight of fluid displaced.” This explains the apparent loss of weight and is fundamental to understanding floatation.
The centre of buoyancy is the centroid of the submerged part where the upthrust acts. Unequal pressure on the upper and lower surfaces of the object leads to a net force upwards because pressure increases with depth.
The pressure at depth h in a fluid of density ρ is given by p = hρg, where g is the acceleration due to gravity.
- Pressure increases with depth in fluids.
- Larger submerged volume causes greater upthrust.
- The force is always upward.
- Upthrust equals weight of displaced fluid.
For more on floating in fluids, review archimedes principle.
Determination of Relative Density by Archimedes Principle
Relative density (specific gravity) of a substance is the ratio of its density to the density of water. It can also be explained as the ratio of its mass or weight to that of water for an equal volume.
| Type | Expression |
|---|---|
| Relative Density (Solid) | $\frac{w_1}{w_1 - w_2}$ |
| Relative Density (Liquid) | $\frac{w_1 - w_3}{w_1 - w_2}$ |
Here, w1 is the body's weight in air, w2 in water, and w3 in another liquid.
Details of these measurements and their significance are further discussed in density vs specific gravity.
Law of Floatation
Floatation is the ability of a body to remain at the surface, or at an upper level, within a fluid. This is observed when the body displaces enough fluid to balance its own weight.
According to the Law of Floatation, a floating body displaces exactly its own weight of the fluid in which it floats. This explains how ships and other floating structures are designed.
- A body’s density must be less than that of the fluid to float.
- The upthrust must equal the object's weight for equilibrium.
- Larger volume allows greater displacement, supporting floatation.
Practical applications of these physical properties are integral to engineering, as well as nature. For additional context, visit understanding buoyancy.
Relation between Upthrust and the Real Weight of the Body
When an object floats, the actual (real) weight is balanced by the upthrust. This means the force upward due to fluid exactly matches the object's weight downward.
The apparent weight of an immersed object is its real weight minus the upthrust. According to Archimedes, this apparent loss in weight equals the weight of fluid displaced, further affirming the law of floatation.
- While floating: real weight = upthrust
- Apparent weight is zero as upthrust balances real weight
- Sinking occurs when real weight exceeds upthrust
Key Physical Quantities and Notations
Many laws related to upthrust use standard quantifiable symbols and SI units. Common terms include force, mass, density, and pressure — all fundamental in JEE physics preparation.
| Symbol | Physical Quantity | SI Unit |
|---|---|---|
| FB | Upthrust | Newton (N) |
| w1, w2, w3 | Weights in air, water, liquid | Newton (N) |
| ρ | Density | kg/m3 |
| g | Acceleration due to gravity | m/s2 |
Understanding different states and properties of matter is useful when analyzing upthrust. Refer to fluid pressure concepts and states of matter overview for related concepts.
JEE-Focused FAQs: Upthrust And Law Of Floatation
The Law of Floatation is used in ship design, hot air balloons, hydrometers, and various engineering applications. In Ferries and submarines, for example, careful manipulation of flotation ensures safety and efficiency.
Buoyancy is temperature-dependent. Heating a fluid decreases its density, lowering upthrust, so objects may sink easier in warmer fluids.
For more practice, explore JEE Main resources by Vedantu, where you can find solved papers and topic-wise notes on these principles.
FAQs on Understanding Upthrust and the Law of Floatation
1. What is upthrust in physics?
Upthrust, also known as buoyant force, is the upward force exerted by a liquid or fluid that opposes the weight of an immersed object.
Key points about upthrust:
- It acts vertically upwards through the center of gravity of the displaced fluid.
- Its magnitude equals the weight of the fluid displaced by the object (as per Archimedes' Principle).
- It explains why objects float or sink when placed in a liquid.
2. State the law of floatation.
The law of floatation states: “An object will float in a fluid if the weight of the fluid it displaces equals the weight of the object.”
In summary:
- If weight of displaced fluid = weight of object, the object floats.
- If weight of displaced fluid < weight of object, the object sinks.
- Floating occurs when upthrust balances the object's weight.
3. What factors affect upthrust exerted on an object?
The upthrust or buoyant force acting on an object depends primarily on:
- Density of the fluid
- Volume of fluid displaced by the object
- Acceleration due to gravity (g)
4. Why do some objects float while others sink?
Objects float or sink in a fluid depending on the relationship between their density and that of the fluid:
- If object density < fluid density, object floats (upthrust > weight).
- If object density > fluid density, object sinks (weight > upthrust).
- The law of floatation governs this behavior.
5. What is Archimedes' Principle?
Archimedes' Principle states that when a body is wholly or partially immersed in a fluid, it experiences an upward force equal to the weight of the fluid displaced.
This principle forms the basis for upthrust and explains floating and sinking of objects.
6. How can you experimentally prove the law of floatation?
To experimentally verify the law of floatation:
- Take an object and measure its weight in air.
- Immerse it in water using a spring balance.
- Record the apparent loss of weight (which equals upthrust).
- Measure the displaced water’s weight.
7. How does the shape of an object affect its floating ability?
The shape of an object can affect its floating by changing how much water it displaces.
- A flatter or hollow shape increases displaced fluid volume, increasing upthrust.
- Objects like ships float because their shape allows them to displace enough water to balance their weight.
8. Explain why a block of iron sinks in water but a ship made of iron floats.
A solid iron block sinks because its density is greater than water and it displaces less water.
- An iron ship is hollow and shaped to displace more water.
- The increased displaced water raises the upthrust to equal the ship’s weight, making it float.
9. What is the formula for buoyant force or upthrust?
The formula for buoyant force (upthrust) is:
Upthrust (F) = Volume displaced (V) × Density of fluid (ρ) × Acceleration due to gravity (g)
This relationship is central to questions on floatation and upthrust in the syllabus.
10. List applications of upthrust and law of floatation in daily life.
Applications of upthrust and the law of floatation are found in:
- Design of boats, ships, and submarines
- Hydrometers to measure liquid density
- Hot air balloons
- Floating of icebergs
- Swimming and aquatic sports
11. What do you mean by apparent loss of weight of a body when immersed in a liquid?
The apparent loss of weight is the difference between the actual weight of a body in air and its weight when fully or partially immersed in a liquid.
- This loss is equal to the upthrust exerted by the liquid.
- It helps in experimentally verifying Archimedes' Principle.
12. Why does ice float on water even though it is made of water?
Ice floats on water because its density is lower than liquid water.
- The structure of ice causes it to occupy more volume, making it less dense.
- This allows ice to displace a weight of water equal to its own, enabling it to float.
