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Question

A fixed cylindrical vessel is filled with water up to height H. A hole is bored in the wall at a depth h from the free surface of water. For maximum horizontal range h is equal to :

A
H
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B
3H/4
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C
H/2
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D
H/4
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Solution

The correct option is C H/2
Let velocity at hole be v , density be ρ. Applying Bernoulli theorem for top-most layer and hole,
Patm+ρgH+1/2ρ02=Patm+ρgh+1/2ρV2
V=2g(Hh)

Time taken to reach ground t=2h/g
Horizontal range
(Horizontalrange) =V×t
=2gH2gh×2h/g

Differentiating Horizontalrange and equating it to zero for maximum Horizontalrange we get maximum Horizontalrange when h=H/2.

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