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. `p_(0)+((6L+H))/(4) dg`
B. `p_(0)+((L+6H))/(4) dg`
C. `p_(0)+((L+3H))/(4) dg`
D. `p_(0)+((L+2H))/(4) dg`

Answer

B

Explanation

`p.A=p_(0)A+`weight of two liquids + weight of cylinder
`=p_(0)A+(H/2)(A)(d)(g)+(H/2)(A)(2d)(g)`
`+L(A/5)((5d)/(4))g`
`:. p=p_(0)+((L+6H))/(4) dg`.