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Question

A cylindrical tank has a hole of area 1 cm2 at its bottom. If water is allowed to flow into the tank from a tube above it at the rate of 70 cm3/sec, then the maximum height up to which water can rise in the tank is -
[Take g=980 cm/s2]

A
2.5 cm
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B
5 cm
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C
10 cm
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D
0.25 cm
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Solution

The correct option is A 2.5 cm
The height of water in the tank becomes maximum when the volume of water flowing into the tank per second becomes equal to the volume of water flowing out per second.

We know, volume of water flowing out per second,
Qout=Av=A2gh .........(1)
where h is the height of water at any instant.
Given, volume of water flowing in per second,
Qin=70 cm3/s .........(2)
From (1) and (2),
A2gh=70
1×2×980×h=70
[ given, A=1 cm2 ]
h=49001960=2.5 cm

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