A container of large uniform cross-sectional area A resting on a horizontal surface, holes two immiscible, non-viscon 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 immeresed such that it floats with its axis vertical at the liquid-liquid interface with length `L//4` in the denser liquid,

The cylinder is then removed and the original arrangement is restroed. a tiny hole of area `s(sltltA)` is punched on the vertical side of the container at a height `h(hltH//2)`. As a result of this, liquid starts flowing out of the hole with a range x on the horizontal surface.
The initial value of x is

Options

A. `sqrt((3H+4h)h)`
B. `sqrt((3h+4H)h)`
C. `sqrt((3H-4h)h)`
D. `sqrt((3H-3h)h)`

Answer

C

Explanation

`t=sqrt((2h)/(g)) implies :. X=vt=sqrt((3H-4h)h)`.