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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

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B

d= density of cylinder
A = area of cross-section of cylinder
Using law of floatation .
Weight of cylinder= Upthrust by two liquids
`L xx A xx d xx g = n rho xx (pL xx A) g + rho (L - pL) Ag`
`d= mp rho + rho (1- p) = (n rho + 1 - p) rho`
`d= {1 + (n-1) p} rho`
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