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Pressure in a fluid-mechanical properties of fluids

Question

Three liquids of densities ρ1,ρ2 and ρ3 and heights as shown are in equilibrium in a U-tube. Match the columns.

Column-IColumn-II
(P) ρ3=2ρ2ρ1(1) K=2h
(Q) ρ3=ρ2ρ12(2) K=h/2
(R) ρ1=ρ2(3) K=0
(S) ρ2=3ρ1+ρ33(4)   None of the above

Moderate
Solution

At the bottom surface of liquid of density is ρ2

ρ1gh+ρ3gKh=ρ2ghρ3=ghρ2ρ1Kgh=ρ2ρ1K

 Compare with ρ3=2ρ2ρ1 or K=12

K=Kh=h2

So, required height of column of density

ρ3=h2

 Now compare with ρ3=ρ2ρ12

K=2 or K=2h

Thus, required height of column of density

ρ3=2h If  ρ1=ρ2,K'=03ρ2=3p1+ρ3 ρ3=3(ρ2p1) or K'=13 K=K'h=h3



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