A container of large uniform cross-sectional area A resting on a horizontal surface, holes 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 the atmosphere having pressure `P_(0)`. A homogeneous solid cylinder of length `L(LltH//2)` and cross-sectional area `A//5` is immersed such that it floats with its axis vertical at the liquid-liquid interface with length `L//4` in the denser liquid,
The density D of the material of the floating cylinder is

Options

A. `5d//4`
B. `3d//4`
C. `4d//5`
D. `4d//3`

Answer

A

Explanation

Weight= upthrust
`:. (L(A)/(5) Dg)=L/4 xx A/5 xx 2d xx g+(3L)/(4) xx A/5 xx dxx g`
`:. D=(5d)/(4)`.