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Two non-mixing liquids of densities rho ...

Two non-mixing liquids of densities `rho` and `nrho(ngt1)` 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(plt1)` 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
Let, the area of cross-secton of the cylinder be A.
Weight of the cylinder = LAgd
Buoyant force on the cylinder due to the liquid of higher density = `pLAnrhog`
and buoyant force on the cylinder due to the liquid of lower density = `(1-p)LArhog`
In equilibrium,
LAgd = `(1-p)LArhog+pLAnrhog`
or, `d=(1-p)rho+pnrho=rho-prho+pnrho`
`therefore" "d=[1+(n-1)p]rho`
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