A `U`-tube in which the cross-sectional area of the limb on the left is one-third of the limb on the right contains mercury (density `13.6 g//cm^(3)`). The level of mercury in the narrow limb extends to a distance of `30 cm` from the upper end of the tube. What will be the rise in the level of mercury in the right limb, if the left limb is filled to the top with water (neglect surface tension effects)?

Explanation

Suppose area of cross section narrow limb be `a` then area of cross section of right limb will be `3 a`

Let the level of mercury in left limb fall be `x` and the rise of level in right limb be `y`, then
`ax=(3a)y`
`x=3y`
According to Pascal's law, `P_(A)=P_(B)`
`(30xx x)rho_(w)g=(x+y)rho_(Hg)g`
`(30xx3y)xx1xxg=(3y=y)xx13.6xxg`
`y=0.58cm`