Question

a column of water 40 cm high supports a 30 cm column of an unknown liquid what is the density of the liquid

Answer 1

Equate the pressure of both water columns
H1Pg = H2P2g
40cm×1 g/cm^3 = 30cm ×X
By Solving
X(Density of unknown liquid) = 1.33g/cm^3

Answer 2

Given: Liquid 1 is water

Height of water column (h₁)= 40 cm

Height of unknown liquid (h₂) = 30 cm

To Find: Density of the unknown liquid

Solution:

Pressure is given as

Pressure = $\frac{Force}{Area}$

Force = Mg, where m is the mass of the liquid and g is the acceleration due to gravity

Pressure = $\frac{Mg}{Area}$

               = $\frac{Volume(Density)(g)}{Area}$                      ( Mass = Volume x Density)

               = $\frac{Area(HeightOfColumn)(Density)(g)}{Area}$                 ( Volume = Area x height)

Pressure = Height of column x density of liquid x g

The density of water is 1000 kg / m³

Since both the columns of liquids support each other, the pressure applied by them should also be the same

P₁ = P₂

h₁ρ₁g = h₂ρ₂g

40 x 1000 = 30 x ρ₂

ρ₂ = $\frac{4000}{3}$ kg / m³

    = 133.33 kg / m³

Therefore, the density of the unknown liquid is  133.33 kg / m³.