A container of large uniform cross sectional area `A`, resting on horizontal surface, holds two immiscible non viscous and incompressible liquids of density `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 tiny hole of area `(s(sltltA)` is punched on the vertical side of the container at a height `h(hltH/2)`. Determine

the initial speed of efflux of the liquid at the hole

Options

A. h=H/3
B. Range R=2H/3
C. Range R=3H/2
D. velocity of efflux r `v=sqrt(2/3 gH)`

Explanation

A,B,D
`H/2xxd+H/2xx3d=Hxx3d`
`rArr H=(2H)/3`
`V_("efflux")=sqrt(2g(H'-h))`
`V_("efflux")` is maximum when h=H'/2
`:. V_(max)=sqrt((2gH)/3)`
Range `R=V_("efflux")xxsqrt((2(H'-h))/g)`
`R_(max)=(2H)/3`