A container of a large uniform cross sectional area A strong on horizontal surface holds two immiscible, non viscous and incompressible liquids of densities `d` and `2d`, each of height `H//2` as shown in the figure. The lower density liquid is open to atmosphere. A homogeneous solid cylinder of length `L(LgtH//2)`, cross sectional area `A//5` is immersed such that it floats with its axis vertical of the liquid liquid interface wit length `L//4` in the denser liquid. Determine a density `D` of the solid and `b` the total pressure at the bottom of the container (atmosphere pressure `=P_(0)`).

Options

A. `5/4d`
B. `4/5d`
C. `4d`
D. `d/5`

Answer

A

Explanation

Weight of clylinder `=` Uthrust due to upper liquid `+` Upthrust due to lower liquid
`impliesD=A/5xxLxxg=d(A/5)[3/4L]g+2d[A/5][L/4]xxg`
`:. (5d)/4`