A vertical U-tube of uniform cross-section contains mercury in both arms A glycerine (relative density =1.3) column of length 10 cm is introduced into one of the arms. Oil of density 800 gm `m^(-3)` is poured into the other arm until the upper surface of the oil and hlycerine are at the same horizontal level, find the length of the column. Density of mercury is `13.6xx10^(3)kgm^(-3)`

Explanation

Pressure at A and B must be same
Pressure at `A= p_(0)+0.1 xx (1.3 xx 1000) xxg`
where `p_(0)` = atmospheric pressure
Pressure at `B=p_(0)+h xx 800 xx g +(0.1 -h) xx 13.6 xx1000 g `
` :. P_(0)+0.1 xx 1300 xxg`
` = p_(0) +800 gh + 1360 g - 13600 xx g xx h `
or `h = 9.6 cm `