2016 Mechanical Properties of FluidsBuoyancy – floating in two immiscible liquids Medium Question 26 of 34 in Mechanical Properties of Fluids

Two non-mixing liquids of densities $\rho$ and $n\rho$ (n > 1) 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 < 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 $\{1 + (n + 1)p\}\rho$

The answer is C.

Solution

Total upthrust from both liquids balances the weight.


Let the cross-section area of the cylinder be A. By Archimedes' principle, upthrust = weight of cylinder:
$n\rho\times A\times pL\times g + A\times(L - pL)\rho g = LA\,dg$
$\Rightarrow LAg(n\rho p + \rho - p\rho) = LAgd$
$\Rightarrow d = \rho\{p(n - 1) + 1\} = \{1 + (n - 1)p\}\rho$

Concept floating-two-liquids

Mechanical Properties of Fluids in past papers

34 questions from this chapter have appeared across 14 exam years.