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Question

A cylindrical vessel of 90 cm height is kept filled up to the brim. It has four holes 1,2,3 and 4 which are, respectively, at heights of 20 cm, 30 cm, 40 cm and 50 cm from the horizontal floor PQ. The water falling at the maximum horizontal distance from the vessel comes from:
119709_a0aa9dc7472e447ea62462d586126611.png

A
hole number 4
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B
hole number 3
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C
hole number 2
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D
hole number 1
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Solution

The correct options are
A hole number 4
B hole number 3
The maximum horizontal distance from the vessel comes from hole numbers 3 and 4. Now, v=2gh, where h is the height of the hole from the top.
Let say height of vessel is 'H'.
The vertical distance travelled by the water is given as Hh=12gt2
We get the time of descent as t=2(Hh)g
Horizontal distance,
x=vt=2gh2(Hh)g=2h(Hh)
Substituting the values we get the maximum distance for hole number 3 and 4.

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