A rectangular-base container floats in water of density ρ w . When it is empty, it is immersed at depth ( D = H /3 ) below the surface. Oil with density ρ 0 is poured into the container until it i

Question

A rectangular-base container floats in water of density $ρ_{w}$ . When it is empty, it is immersed at depth $(D = H /3)$ below the surface. Oil with density $ρ_{0}$ is poured into the container until it is about to sink. At this instant, height of oil from the base of container is $2 H / n$ . Find n . (Take $ρ_{w} = \frac{3 ρ _{0}}{4}$ )

TestHub · Accepted Answer

Empty container: m g = ρ w ​ g A 3 H ​ About to sink with oil of height 2H/n: m g + ρ 0 ​ g A n 2 H ​ = ρ w ​ g A H Subtracting and using ρ w ​ = 4 3 ρ 0 ​ ​ : n 2 ρ 0 ​ ​ = 3 2 ρ w ​ ​ = 2 ρ 0 ​ ​ ⇒ n = 4 . Answer: 4

Physics - Fluid Question with Solution | TestHub

Doubts & Discussion