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 speed of efflux without cylinder is

Options

A. `v=sqrt((g)/(3)[3H+4h])`
B. `v=sqrt((g)/(3)[4H-3h])`
C. `v=sqrt((g)/(3)[3H-4h])`
D. None of these

Answer

C

Explanation

Applying Bernoulli's equation just inside and just outside the hole.
`p_(0)+(H/2)(d) g+(H/2-h)(2d)(g)=1/2(2d)v^(2)+p_(0)`
`:. v=sqrt(g/2 (3H-4h))`.