Archimedes Principle - Meaning, Experiments, Examples, FAQs

What is Archimedes' Principle?

According to Archimedes' principle:

Archimedes principle definition and Archimedes meaning: The Archimedes principle is named after the Greek mathematician “Archimedes of Syracuse”. The phenomenon that a partly or fully submerged object appears to be lighter than its actual weight is equal to the weight of the liquid displaced by the object.

Every type of fluid will exert pressure in all directions equally. This pressure is produced by the weight of the fluid. A fluid exerts an upward pull on an object when it is partially or completely submerged in it. This upward force is known as buoyant force, making the object seem lighter.

The weight of the fluid displaced by the object = Reduced weight

Archimedes created this relationship. The law of buoyancy is useful in everything from large ships to small boats, planes, and submarines.

Also read -

• NCERT Solutions for All Subjects

Apparent Weight

The apparent weight of an object is the weight of the body experienced by it when it is submerged in a fluid. When a body is placed in a fluid, it experiences an upward push (buoyant force), which reduces the downward pull and makes the object feel lighter than its actual weight. If an object is floating on the surface then it weight feels almost negligible.

Let's understand the phenomenon by an example:

When you have a big stone in water, its weight is lighter than when you experience it on land. This is because water offers a buoyant force(upthrust) making an object feel lighter.

Apparent weight = Actual weight - Buoyant force

Explain Archimedes' Principle Derivation

The idea is based on the buoyancy principle, which asserts that any item fully or partially immersed in a gas or liquid can exert an upward pull on it. The buoyant force refers to the upward thrust.

A cylinder of height h and radius r is immersed vertically in a liquid in the diagram above, with its flat surfaces at depths h1 and h2, and h1 < h2. At each point on the cylinder's surface, the liquid exerts a perpendicular thrust (pressure). The net thrust on the curved surface is zero due to axial symmetry. The downward pressure on the upper flat surface is h₁ρg, where g is the gravitational acceleration and ρ is the density of the liquid.

$h_2 \rho g$ of upward pressure is exerted on the bottom flat surface. The downward force on the upper surface, if the air pressure is Patm, is

$$
F_1=\left(P a t m+h_1 \rho g\right) \pi r^2
$$

On the bottom surface, the upward force is,

$$
F_2=\left(P a t m+h_2 \rho g\right) \pi r^2
$$

The resultant force on the cylinder is upward and the magnitude is, since $\mathrm{h} 1<\mathrm{h} 2$

$$
\begin{aligned}
& \mathrm{Fb}=\mathrm{F}_2-\mathrm{F}_1 \\
& \mathrm{Fb}=\left(\mathrm{h}_2-\mathrm{h}_1\right) \rho \mathrm{g}_1 \mathrm{r}^2
\end{aligned}
$$

The upward thrust can be stated as, where $\mathrm{h}=\mathrm{h} 2-\mathrm{h} 1$ is the cylinder's height and $V=\pi r^2 h$ is its volume.

$$
\mathrm{Fb}=\rho \mathrm{V} g
$$

The weight of liquid of equal volume V as the submerged object is the right-hand side of this upthrust Archimedes principle formula. The buoyant force, on the other hand, has the same magnitude as the apparent weight loss of the object. As a result, the apparent drop in object weight equals the weight of the fluid displaced by the object.

Archimedes Principle Experiments

1. Fill a cup to the full with water and set it in an empty dish.

2. Now, grab whatever solid object you want and weigh it with a spring balance. Make a note of it.

3. Submerge the object in the water while it is still attached to the spring balance. Simply ensure that the spring balance is not immersed.

4. Take note of the weight displayed by the spring balance now. You'll notice that it's decreased. A certain amount of water will be displaced into the bowl.

5. Collect and weigh this water. You'll notice that the weight loss of the object is exactly equal to the weight loss of the water!

Law of Floating-

The magnitudes of the object's real weight W1 and the buoyant force W2 exerted by the fluid determine whether an immersed object will float or sink.

1. W1 > W2: The object's resultant force is downward, causing it to sink. This condition occurs when the object's density is larger than the fluid's density.

2. W1 = W2: The real weight and buoyant force are similar when the densities of the object and the fluid are equal. In a totally immersed state, the object can float at any depth.

3. W1 <W2: The net force works in an upward direction, causing the object to be partially submerged. In such instances, the object's density is lower than that of the fluid.

Application of Archimedes Principle

The Archimedes principle has the following applications:

1. Submarines remain completely submerged because of the ballast tank. The ballast tank is the part of the submarine that is filled with water and makes it heavier. This weight makes the submarine heavier than the buoyant force acting on it and keeps it submerged.

2. Hot-air balloon: Because the buoyant force of the hot-air balloon is less than that of the surrounding air, hot-air balloons rise and float in mid-air. When the hot-air balloon's buoyant force is greater, it begins to drop. This is accomplished by adjusting the amount of heated air in the balloon.

3. A hydrometer is a device that is used to determine the relative density of liquids. The hydrometer is made up of lead bullets that float vertically in the liquid. The deeper the hydrometer sinks, the lower the liquid density.