Question

Two non-mixing liquids of densities ⍴ and n⍴(n > 1) are put
in a container. The height of each liquid is h. A solid cylinder
of length L and density d is put in this container. The cylinder
floats with its axis vertical and length pL(p < 1) in the denser
liquid. The density d is equal to : [2016]
(a) {1 + (n + 1)p}⍴ (b) {2 + (n + 1)p}⍴
(c) {2 + (n – 1)p}⍴ (d) {1 + (n – 1)p}⍴

Answer 1

Answer:

Using Archimedes' principle, we get:

LAdg=(pL)A(nρ)g+(1−p)LAρg

⇒d=(1−p)ρ+(pn)ρ

         =[1+(n−1)p]ρ