A U -tube in which the cross - sectional area of the limb on the left is one quarter, the limb on the right contains mercury `(density 13.6 g//cm^3).` The level of mercury in the narrow limb is at a distance of 36 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 ?

Options

A. `1.2cm`
B. `2.35cm`
C. `0.56cm`
D. `0.8cm`

Answer

C

Explanation

Let the rise of level in the right limb be `x cm`. the fall of the level of mercury in the left limb be `4x`.
Therefore, the level of water in the left limb is `(36+4x)` cm.
Equating pressure at the interface of mercury and water, we have (at `A_(1)` and `B_(1))`
`(36+4x)xx1g=5xx13.6xxg`
Solving we get `x=0.56cm`