1.

Two communicating vessels contain mercury. Thediameter of one vessel is four times larger than the diameter of the other. A column of water of height h0 = 70 cm is poured into the left hand vessel (the narrower one). How much will be mercury level rise in the right hand vessel ? (Specific density of mercury = 13.6)

Answer»

Let us assume that , if the level of narrow tube goes down by h_1 then, WIDER tube goes up by h_2
then, volume DECREASES in CASE of narrow tube = volume increases in case of wider tube

Let RADIUS of narrow tube is r
then, radius of wider tube is 4r

so, \pi r^2h_1=\pi(4r)^2h_2

h_1=16h_2.......(1)

now, pressure at point A = pressure at point B
h\rho g=(h_1+h_2)\rho' g

because specific DENSITY , s = \rho'/\rho
so, h=(h_1+h_2)s

h=16h_2+h_2

h_2=\frac{h}{17s}=\frac{70}{17\times13.6}=0.3


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