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Question

There are two identical small holes of area of cross section a on the opposite sides of a tank containing a liquid of density ρ. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which has to be applied on the tank to keep it in equilbrium is :
71918_2b1475fb665a4c8e8ef7020248d2ce07.png

A
ghρa
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B
2ghρa
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C
2ρagh
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D
ρgha
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Solution

The correct option is D 2ρagh
Momentum of the mass of water coming out of the hole per sec is thrust.
Resultant thrust F=F1F2=ρav21ρav22=ρa2gh1ρa2gh2=2aρg(h1h2)
horizontal force that has to be applied to the tank to keep it in equilibrium is
2aρg(h1h2)
or
2aρgh
137720_71918_ans_4dab16173894402ea8266ff8399ceef2.png

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