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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`

B

`{1+(n-1)p]p`

C

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

D

`{2+(n+1)p]p`

Text Solution

Verified by Experts

The correct Answer is:
B
The liquid with higher density np will settle down first in comparison to the liquid of density p as shown in figure. The length pL is immersed in denser liquid and the cylinder is floating.
Using the concept of Aarchimedes principle
Weight of cylinder =Weight of dipsplaced liquid of density np+Weight of displaced ilquid of density p.
`LAdg=(pL) A eta pg+(1-p)LA pg`
`d=(1-p)p+ppn=p+pnp-pp`
`=[1+(n-1)p]p`
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