### Archimedes Principle Calculator :

Enter the Archimedes’ principle calculator, you can measure the density of a crown or study the changes in mass and weight of a submerged, and you check the calculator.

### Archimedes Principle Formula :

Archimedes principle formula is the buoyant force F_{b(N)} in Newton is equal to the product of the density of the fluid ρ_{(kg/m3)} in kilogram per meter3 and multiply the acceleration due to gravity g_{(m/s2)} in meter per second2 and multiply the submerged volume v_{(mL)} in meter per length. Hence the Archimedes principle formula can be written as,

**F _{b(N)}=ρ_{(kg/m3)}*g_{(m/s2)}*v_{(mL)}**

Where,

F_{b} → buoyant force in Newton

ρ → density of the fluid in kg/m3

V→ submerged volume in mL

G→ acceleration due to gravity in m/s2

Therefore the mass of the displaced liquid can be written as follows,

Mass(M)= Density (ρ)* volume(v)

Weight =Mass*Acceleration due to gravity

Weight=Mass*g= ρ* v*g

From Archimedes principle we know that the apparent loss of weight is equal to the weight of the water displaced therefore the thrust force is given by the following equation

Thrust Force = ρ* v*g

### Sums :1

Calculate the resulting force if a steel ball of radius 8cm is immersed in water?

### Answer :

Given,

Radius of steel ball =8cm=0.08m

Volume of steel ball

v=4/3 π*r^{3}

V=4/3*3.14*0.08^{3}

V=21.4*10^{-4} m^{3}

Density of water ρ=1000 kg m^{-3}

Acceleration due to gravity g=2.14 ms^{-2}

From Archimedes principle formula

F_{b(N)}=ρ_{(kg/m3)}*g_{(m/s2)}*v_{(mL)}

F_{b}=(1000 kg m^{-3})(2.14 ms^{-2})( 21.4*10^{-4} m^{3})

F_{b}=4.57N

### Sums :2

Calculate the buoyant force? In a floating body is 85% submerged in water. The density of water is 2000 kg.m^{-3}.

### Answer :

Given,

Density of water ρ=2000kg m^{-3}

From Archimedes principle formula

F_{b(N)}=ρ_{(kg/m3)}*g_{(m/s2)}*v_{(mL)}

Or

V_{b}*P_{b}*g= ρ*g*v

Where

ρ,g and v are the density , acceleration due to gravity and volume of the water

V_{b},P_{b} and g are the volume , density , and acceleration due to gravity of body immersed

Rearranging the equation

P_{b} =V ρ /v_{b}

Since 85% of the body is immersed

0.85* v_{b} =V

P_{b}=850kg m^{-3}