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Two non-mixing liquids having densities p and 2p 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 vertical axis and half of the cylinder is in the denser liquid. What is density d in terms of p. Check attached image for clarification.

Two non-mixing liquids having densities p and 2p 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 vertical axis and half of the cylinder is in the denser liquid. What is density d in terms of p.
 
Check attached image for clarification.

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Grade:9

1 Answers

Arun
25750 Points
6 years ago
Given that the cylinder is floating in two liquids. Given that the length of the cylinder is L and it is having a part ρL in the denser liquid. So,

ρgAL=AρLndg+A(1−ρ)Ldg⇒ρ=ρnd+(1−ρ)d ⇒ρ=ρnd+d−ρd⇒ρ(1+d−nd)=d ⇒ρ=d/(1+d−nd)⇒ρ=d/1+d(1−n) 
 
Now put n = 2
 
Hence density = d/1 -d

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