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A simple U tube contains mercury to the same level in both of its arms. If water is poured to a height of 13.6 cm in one arm, how much will be the rise in mercury level in other arm? Density of mercury 13.6×103kg/m3 and density of water = 1000kg/m3.

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Solution

Initially, the length of mercury columns in two arms is equal.

Height to which water is poured in one arm, h = 13.6 cm

Density of mercury = 13.6 × 103 kg m-3

Density of water = 103 kg m-3


Pouring 13.6 cm water, the mercury level goes down to A, by x cm in the left arm and rises to C, by x cm in the right arm. So, BC=2x cm

Pressure at level A = Pressure at level B

or 13.6 × 103 × g = 2x × 13.6 × 103 × g

2x = 1 cm

The rise in mercury level in the other arm will be x= 0.5 cm.


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