A vertical U-tube of uniform cross-section contains mercury in both its arms. A glycerine (density = 1.3g*cm^(-3)) column of height 10 cm is introduced into one of the arms. Oil of density 0.8g*cm^(-3) is poured into the other arm until the upper surfaces of oil and glycerine are at the same level. Find the height of the oil column. The density of mercury is 13.6g*cm^(-3).

A vertical U-tube of uniform cross-section contains mercury in both it

1.	A vertical U-tube of uniform cross-section contains mercury in both its arms. A glycerine (density = 1.3gcm^(-3)) column of height 10 cm is introduced into one of the arms. Oil of density 0.8gcm^(-3) is poured into the other arm until the upper surfaces of oil and glycerine are at the same level. Find the height of the oil column. The density of mercury is 13.6g*cm^(-3).
Answer» Solution :Let the height of the oil column be H ACCORDING to the figure, AC = ED or, h + BC = 10 or, BC = (10 - h)cm Now, PRESSURE at the point C = pressure at the point D or, `hxx0.8xxg+(10-h)xx13.6xxg=10xx1.3xxg` or, `hxx0.8+136-13.6h=13` or, 12.8h = 123 or, `h=123/12.8=9.61`cm.