Properties Of Solids And Liquids Question 199

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 $ \rho $ . The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

Options:

A) $ gh\rho a $

B) $ \frac{2gh}{\rho a} $

C) $ 2\rho agh $

D) $ \frac{\rho gh}{a} $

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Answer:

Correct Answer: C

Solution:

Net force (reaction) = $ F=F _{B}-F _{A} $

$ =\frac{dp _{B}}{dt}-\frac{dp _{A}}{dt} $

$ =av _{B}\rho \times v _{B}-av _{A}\rho \times v _{A} $

$ F=a\rho \left( v _{B}^{2}-v _{A}^{2} \right)

$ -(i)

According to Bernoulli’s theorem $ p _{A}+\frac{1}{2}\rho v _{A}^{2}+\rho gh=p _{B}+\frac{1}{2}\rho v _{B}^{2}+0 $

therefore $ \frac{1}{2}\rho \left( v _{B}^{2}-v _{A}^{2} \right)=\rho gh $ therefore $ v _{B}^{2}-v _{A}^{2}=2gh $ From equation (i), $ F=2a\rho gh. $



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