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Question

A cylindrical vessel of 90 cm height is filled upto the brim. It has four holes 1, 2, 3, 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

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
In general, from Toricelli's theorem velocity of efflux v=2gh where h is depth of hole from water surface.


Range of the water falling on surface PQ from a hole at a depth of h below surface is
R=v2(Hh)g (where v=2gh)
R=2h(Hh)


Now substituting h for different holes

For Hole (1):
Hh=20 cm, h=70 cm
R1=270(20) cm=2014 cm
For Hole (2):
Hh=30; h=60
R2=230(60) cm=2018 cm
For Hole (3):
Hh=40; h=50
R3=240(50) cm=2020 cm
For Hole (4): Hh=50; h=40
R4=250(40) cm=2020 cm
Thus
R4=R3>R2>R1

Options A,B are correct

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