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Question

A cylindrical vessel is filled with a liquid up to a height H. A small hole is made in the vessel at a distance y below the liquid surface as shown in figure. The liquid emerging from the hole strikes the ground at distance X.


A
X remains same if the hole is at depth y or Hy.
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B
X is maximum for y=H2.
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C
both (a) and (b) are correct.
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D
both (a) and (b) are wrong.
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Solution

The correct option is C both (a) and (b) are correct.
We know, range of efflux from the hole is given by -
X=2y(Hy)
If hole is made at depth y=Hy, then
X=2(Hy)[H(Hy)]
=2y(Hy)
=X
Hence, range will remain same.


Now, dXdy=12(yHy2)1/2(H2y)
For maximum value of X, dXdy=0
H2y2(yHy2)1/2=0
[Since denomenator can't be zero, y0 & yH]
y=H2
Both statements are true.
So, option C is correct.

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