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Two non-mixing liquids of densities rho ...

Two non-mixing liquids of densities `rho` and `(n gt1)` 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 lt 1)` in the denser liquid. The density `d` is equal to :

A

`{2+(n+1)p}rho`

B

`{2+(n-1)p}rho`

C

`{1+(n-1)p}rho`

D

`{1+(n+1)p}rho`

Text Solution

Verified by Experts

The correct Answer is:
c
According to question, the situation can be drawn as following. Applying Archemedies principle
Weight of cylinder `= ("upthrust")_(1) + ("upthrust")_(2)`
i.e., `Aldg = (1-P) Larho g + (PLA)n rho g`
`rArr d = (1-P)rho+Pn rho = rho-P rho + n P rho`
`= rho + (n-1) P rho = rho[1+(n-1)rho]`
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