Question

a simple u tube contains Mercury to the same level in both arm . if water is poured to the a height of 13.6 cm in one arm , how much will be the rise in mecury level in other arm? given:13.6×10^3kgm-3density of mecury &10^3 kgm-3 density of water

Answer 1

When water is added to one side of the U tube, the rise in mercury level of the other side of the U tube will be depend on the density of water and mercury.

The height of water added in one arm = 13.6cm, we have to calculate the corresponding rise in level in the other arm

The pressure difference tn the two arms will be equal

So, the pressure difference in water column = the pressure difference in the other arm or mercury

                     i.e. hHg d g  = hW d g

                          hHg    = hW×density of water × g ÷ density of mercury × g

                                  = 13.6cm × 1000kg/m3 × g ÷ 13.6 × 1000kg/m3 × g

                                  = 1cm

i.e. When 13.6cm water is added to one arm of the U tube, only a height of 1cm will be the rise in mercury level in the other arm. 

Answer 2

This may help you!

The main twist in this question was the increase level is not of x but of 2x

Check the image below all the doubts of yours would clarify