question_answer

A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/cm3) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/cm3 is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm3

A)            10.4 cm

B)            8.2 cm

C)            7.2 cm

D)            9.6 cm

Correct Answer: D

Solution :

                                      At the condition of equilibrium                    Pressure at point A = Pressure at point B                    \[{{P}_{A}}={{P}_{B}}\]Þ \[10\times 1.3\times g=h\times 0.8\times g+(10-h)\times 13.6\times g\]            By solving we get h = 9.7 cm