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A container of large uniform cross secti...

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

a.the initial speed of efflux of the liquid at the hole
b. the horizontal disance `x` travelled by the liquid initially
c. the height `h_m` at which at the hole should be punched so that the liquid travels the maximum distance `x_(m)` initially. also calculate `x_(m)` (neglect air resistance in calculations).

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Verified by Experts

The correct Answer is:
[(i) `v = sqrt((g)/(2)(3H - 4h))]`, (ii) `sqrt([(3H-4h)h])` , (iii) `sqrt([(3H-(4 xx 3)/(8)H)(3)/(8)H]) = (3H)/(4)`]
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