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Question

Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel?


A

H/4

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B

H/2

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C

H/2

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D

H/3

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Solution

The correct option is C

H/2


Let the hole is made at a height 'h' above the bottom.

Let the water spurts out through the hole with velocity 'v'.

By Torricelli's equation

v=2g(Hh)
Time taken by this get to reach the bottom,
h=12gt2
t=2hg
Now horizontal distance covered by stream of water in this time interval,
x=(2g(Hh))x2hg
x=2h(Hh)
Maximizing x is same as maximizing x2 as it is the distance.
d(x2)dh=2H4h=0
H=H2

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