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Question
A cylinder containing water up to a height of 24 cm has a hole in its bottom. It is counter-poised in a balance. When water begins to flow out, the initial decrease in balancing weight is required to be 12 gf to keep the balance beam horizontal. The cross-sectional area of the hole is :
A cylinder containing water up to a height of 24 cm has a hole in its bottom. It is counter-poised in a balance. When water begins to flow out, the initial decrease in balancing weight is required to be 12 gf to keep the balance beam horizontal. The cross-sectional area of the hole is :
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Solution
The correct option is A 0.25 cm2
From Toricellis theorem v=√2ghSo, force exerted by the let of liquid on cylinder =fav2 ...........(1) [where a is cross sectional area]Decrease in balancing weight =2gh.............(2)So, in order to balance,(1)=(2)λa,2g×24=12×g⇒a=122×24cm2⇒a=0.25cm2
From Toricellis theorem v=√2gh
So, force exerted by the let of liquid on cylinder =fav2 ...........(1) [where a is cross sectional area]
Decrease in balancing weight =2gh.............(2)
So, in order to balance,
(1)=(2)
λa,2g×24=12×g⇒a=122×24cm2⇒a=0.25cm2
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