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Question

A liquid X of density 3.36 g/cc is poured in a U tube (containing mercury) in the right arm upto height 10 cm above the mercury level. Another liquid Y is poured in the left arm upto height 8 cm as shown in figure. Upper levels of X and Y are the same. What is the density of liquid Y? [Take ρHg=13.6 g/cc]



Correct Answer
A
0.8 g/cc
Your Answer
B
1.2 g/cc
Your Answer
C
1.4 g/cc
Your Answer
D
1.6 g/cc

Solution

The correct option is A 0.8 g/cc
Pressure at same level in the same liquid will be equal.
Hence, in the two arms of the Utube, pressure will remain same on the surface PP,as shown in figure.


Patm+ρ1gh1+ρ2gh2=Patm+ρ3gh3 ...(i)
Here,
Patm= atmospheric pressure acting on the open ends of Utube
ρ1=density of liquid Y
h1=8 cm
ρ2=ρHg=13.6 g/cc
h2=108=2 cm
ρ3=ρX=3.36 g/cc
h3=10 cm
Substituing in Eq.(i),
Patm+(ρ1×g×8)+(13.6×g×2)=Patm+(3.36×g×10)
8ρ1+2×13.6=10×3.36
ρ1=33.627.28=0.8 g/cc

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