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} $
Show Answer
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. $
