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)/(4) d `
B. ` (4)/(5) d `
C. ` 4d `
D. ` (d)/(3) `

Answer

A

Explanation

Weight of cylinder = Upthrust due to upper liquid + upthrust due to lower liquid
`rArrD((A)/(5))xxLxxg=d((A)/(5))[(3)/(4)L]g+2d[(A)/(5)][(L)/(4)]xxg" "therefore" "D=5d//4`