Two identical containers A and B are filled with two different liquids of equal masses. The level of the liquid in container A is found to be one-fourth of the level of the liquid in container B. What is the ratio of thedensity of two liquids? If the density of he liquid in the container A is 2 " g "` cm^(-3)`, then find the density of the mixture of the two liquids.

Explanation

Mass of liquid A, `(m_(A))` = mass of liquid B, `(m_(B))`
Volume = `area xx height`
Area of cross section of A = Area cross section of B
Height of liquid column A = `1/4 xx` " height " of liquid column A = `1/4 " (Volume of B) "
Density of `"mass/volume"` `(density " of " A)/(density " of " B) = m_(A)/V_(A)xx V_(B)/m_(B)=V_(B)/V_(B)=4/1=4 :1`
If density of A is 2 " g " `cm^(-3)` ,then density of B = " g " `cm^(-3)` = 0.5 " g " `cm^(-3)`
Density of mixture = `"mass of mixture"/"volume of mixture"`
`(m_(A)+m_(B))/(v_(A)+v_(B))=(m_(A)=m_(A))/(v_(A)=4v_(A)) ( :. m_(B) = m_(A) and v_(B)= 4v_(A))`
`(2m_(A))/(5v_(A)) = (2xx d_(A)xx v_(A))/(5V_(A)`
`(2xx2)/5=4/5=0.8 " g "cm^(-3)`