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 ρ . 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) ghρa

B) 2ghρa

C) 2ρagh

D) ρgha

Show Answer

Answer:

Correct Answer: C

Solution:

Net force (reaction) = F=FBFA

=dpBdtdpAdt

=avBρ×vBavAρ×vA

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

$ -(i)

According to Bernoulli’s theorem pA+12ρvA2+ρgh=pB+12ρvB2+0

therefore 12ρ(vB2vA2)=ρgh therefore vB2vA2=2gh From equation (i), F=2aρgh.



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