Determine height h of oil in the U tube as shown in figure. Density of oil =0.9g/cc; density of liquid is 1.6g/cc and density of mercury =13.6g/cc.
A
9.45cm
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B
18.9cm
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C
27.2cm
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D
16.1cm
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Solution
The correct option is B18.9cm Given:
density of oil =ρo=0.9g/cc
density of mercury =ρm=13.6g/cc
density of liquid =ρL=1.6g/cc
In equilibrium state, the pressure due to the same level of the same liquid must be equal.
Taking pressure at level C in both arms of the U tube, we have Pressure due to hcm of oil + pressure due to (20−h)cm of mercury = pressure due to 20cm of liquid
i.e. ρ0gh+ρmg(20−h)=ρLg(20) ⇒0.9×g×h+13.6×g×(20−h)=1.6×g×20 ⇒0.9h+272−13.6h=32 ⇒12.7h=240 ∴h=24012.7=18.9cm