Looking for classes? Ksquare Career Institute, Bengaluru →
Mechanical Properties of Fluids
Buoyancy – floating in two immiscible liquids
1 question from 1 paper, each with its answer.
- question
- 1
- paper
- 1
- of Mechanical Properties of Fluids
- 2.94%
Concepts tested
- floating-two-liquids
All Questions
2016 1 question
-
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
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:
$n\rho\times A\times pL\times g + A\times(L - pL)\rho g = LA\,dg$
$\Rightarrow LAg(n\rho p + \rho - p\rho) = LAgd$
$\Rightarrow d = \rho\{p(n - 1) + 1\} = \{1 + (n - 1)p\}\rho$
