question_answer

A liquid X of density \[3.36\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]is poured in a U-tube, which contains Hg.

Another liquid Y is poured in left arm with height 8 cm, upper levels of X and Y are same.

What is the density of V?

 

A) \[0.8\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]     

B) \[1.2\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]

C) \[1.4\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]       

D) \[1.6\,\text{g}\,\text{c}{{\text{m}}^{-3}}\]

Correct Answer: A

Solution :

[a]: As     shown in adjacent figure, in  the two arms of a tube  pressure remains same  on surface PP'.            Hence, \[8\times {{\rho }_{Y}}\times g+2\times {{\rho }_{Hg}}\times g=10\times {{\rho }_{X}}\times g\] \[\therefore \]\[8{{\rho }_{Y}}+2\times 13.6=10\times 3.36\] or\[{{\rho }_{Y}}=\frac{33.6-27.2}{8}=0.8g\,c{{m}^{-3}}\]