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Two non-mixing liquids of densities rho ...

Two non-mixing liquids of densities `rho` and `nrho` `(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 Archimedes principle,
Weight of cylinder `=("upthrust")_(1)+("upthrust")_(2)`
i.e., Aldg=`(1-p)Larhog+(pLA)nrhogs`
`rArr d=(1-p)rho + pnrho=rho-prho+nprho`
`=rho+(n-1)prho=rho[1+(n-1)p]`
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