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 corss section of A=Area of cross section of B
Height of liquid column `A=1/4 xx" height of liquid Column B"`
volume of `A=1/4 ("Volume of B")`
Density `=("mass")/("volume")`
`("density of A")/("density of B")=(m_(A))/(V_A) xx V_B/m_B=V_B/(V_(B)/4)=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)) (therefore m_(B)=m_(A) and v_(B)=4v_(A))`
`=(2m_A)/(5v_(A))=(2 xx d_(A) xx v_(A))/(5V_(A))`
`=(2 xx 2)/(5)=4/5 =0.8 g cm^(-3)`