Archimedes Principle
We know that due to upthrust, objects tend to lose weight when immersed in liquid. Archimedes principle states that "If an object is partially or completely immersed in the liquid, the weight of liquid displaced by the object is its upthrust". This law is applicable for the gaseous medium too.The weight of the displaced liquid = ρgv where ρ is density of the liquid, g is acceleration due to gravity and v is the volume of the displaced liquid.
Law of Flotation:
Law of flotation states that "The weight of the liquid displaced by a floating object is equal to its weight". When an object sinks it displaces liquid, as it is sinking the amount of water displaced increases (Archimedes principle) until it displaces liquid as much as its weight. If the object displaces liquid equals to its weight the object floats if it cannot then the object sinks.
If a wooden cork is subjected to the water, the water displaced by the cork is very less but is equal to its weight. So it easily floats in water. If a rubber cork is subjected to water then the water displaced by the rubber cork is larger as its weight is also greater than wooden cork. So it also floats. But if we use the cork made by stone it sinks because it cannot displace water equal to its weight.
Hydrometer:
It is the instrument used to measure specific gravity of the liquids. It is based on the principle of flotation. There are two types of hydrometer
Constant immersion hydrometer:
This is also called Nicolson hydrometer because it was invented by him.
Construction:
In this hydrometer, a metallic rod with a mark on it connected is a pan as shown in figure. At the lowest part, a heavy cone filled with lead is connected to help it remain vertically inside liquid. This instrument is used to measure relative density of liquids.
Working:
To measure relative density of a liquid, it is kept in the liquid and by adding weights in its pan the mark on the rod is managed to bring at the surface of the liquid. On the basis of the amount of weight required to maintain the level, relative density of the liquid is analyzed.
Constant weight hydrometer:
Construction:
It consists of a hollow cylindrical glass build. Its lower portion is filled with lead shots and they are fixed in the position using sealing wax. The cylindrical bulb is heavy helps the hydrometer to float in a liquid vertically. A graduated stem is at the top. The stem is made narrow for greater sensitivity.
Working:
When a hydrometer is placed in a liquid, it sinks until it displaces the liquid which is equal to its own weight. The stem is graduated in kg/m3 to give the value of density and sinks more in the liquids having less density. Thus, the constant weight hydrometer measures the density of liquid directly without calculation. A specially designed constant weight hydrometer used to test the purity of milk is known as lactometer.
 Archimedes principle states that "If an object is partially or completely immersed in the liquid, the weight of liquid displaced by the object is its upthrust".
 Law of flotation states that "the weight of the liquid displaced by a floating object is equal to its weight".
 Hydrometer is the instrument used to measure specific gravity of the liquids.
 A specially designed constant weight hydrometer used to test the purity of milk is known as lactometer.
The balloon filled with hydrogen is rising because the weight of the balloon filled with hydrogen is less than the weight of air displaced by it i.e. upthrust of the atmosphere is acting on the balloon. As we go up in the atmosphere the density of air decreases that leads to decrease in the weight of displaced air i.e. decrease in the upthrust. As the weight of the hydrogen balloon is same to the weight of air displaced by it, it stops to rise.
Given,
Density of wood(d_{1})= 800kg/m^{3}
Density of water (d_{2})=100kg/m^{3}
Volume of wood(V)=1.6m^{3}
Mass of wood (m)= d_{1}×v
=800×1.6
=1280kg
Now,
Mass of displaced water=mass of wood=1280kg
\begin{align*} \text{Volume of wood, sinking on water}&= \text{volume of displaced water} \\&=\frac{\text{mass of displaced water} }{\text{density of water}}\\ &= \frac{1280kg}{1000kg/m^3}\\ &= 1.28 \: m^3\end{align*}
\begin{align*}\text{Sinking part of wood} &= \frac{\text{Volume of wood sinking on water}}{\text{Volume of wood}}\\ &=\frac{1.28m^3}{1.6m^3}\\&= 0.8 \end{align*}
Here,mass of a brick(m1) = 2 kg
Density of the brick (d_{1}) = 2.5 g/cm^{3} = \(\frac {2.5 × 10^{3} kg}{10^{6} m^3}\)
= 2500 kg/m^{3}
∴ Volume of the brick (V_{1}) = \(\frac{mass}{density}\)
= \(\frac{2}{2500}\)
∴ Mass of the displaced water is 0.8 kg.
= \(\frac{1}{1250}\)m^{3}
^{H}ere,mass of brick (m_{1}) = 2 kg
Density of brick(d_{1}) = 2.5g /cm^{3}
= 2500 kg/m^{3}
Density of water (d_{2}) = 1000 kg/m
Mass of water displaced = (m_{2}) = ?
For sinking bodies
V_{1}=V_{2}
or, \(\frac{m_1}{d_1}\)=\(\frac{m_2}{d_2}\) [∴d=\(\frac{m}{v}\) ]
∴ \(\frac{d_1}{d_2}\)=\(\frac{m_1}{m_2}\)
\(\frac{2500}{1000}\)
\(\frac{2}{m_2}\)
∴ m_{2} =\(\frac{1000×2}{2500}\)
= \(\frac{20}{25}\)
= \(\frac{4}{5}\)
= 0.8 kg
∴ Mass of the displaced water is 0.8 kg.
Pascal's law states that liquid exerts pressure equally in all directions.
Given,
Depth of water (h) = 6m
Density of water (d) =1000 kg /m^{3}
Acceleration due to gravity (g) = 9.8/sec^{2}
Pressure of water (p) =?
We know,
p=h× d× g
=6 × 1000×9.8
=58800Pa
Hence, the water pressure exerted at the bottom of the tank is 58800 Pascal.

The buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by that object is ______.
Archimedes' principle
Pascal's principle
Bernoulli's principle
Hooke's principle

Which one is also called Nicolson hydrometer?
hydrometer
Constant weight hydrometer
Constant immersion hydrometer
None of these

Which instrument is used to measure relative density of liquids?
None of these
Constant immersion hydrometer
Constant weight hydrometer
both of these

which instrument used to measure specific gravity of the liquids?
byarometer
Constant weight hydrometer
Constant immersion hydrometer
hydrometer

Archimedes principle law is applicable for the ______.
gaseous medium too
Law of Flotation
gravity too
pressure too

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