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Question

A vertical U tube of uniform inner cross-section containing mercury in both its arms. A glycerine ( density 1300kgm3) column of length 10 cm is introduced into one of the arms. Oil of density (800kgm3) is poured in the other arm until the upper surface of the oil and the glycerine are in the same horizontal surface. Find the length of oil column ( Density of mercury = 13.6×103kgm3)
1104944_5607dda3a56a4532a68aa4be5b624c2d.PNG

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Solution

REF.Image.
as point A and B are at
horizontal level,
Pressure at A=fuly×g×20100
PA=1300×10×20100
PA=2600N/M2
Pressure at B =foil×g×h+fHh×g×(20h)100
PB=800×10×h100+13.6×103×10×(20h)100
PB=80h+1360(20h)
As PA=PB,
2600=80h+272001360h
1280h=272002600
1280h=24600
h=246001280=1921875
h=19.22cm
The length of oil column is 19.22 cm.

1112468_1104944_ans_7619aedd418b43feb787c3a0bf907bec.jpg

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