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Question

What length of water column in a given tube has equivalent pressure to 0.86 m of mercury column? The density of mercury is 13.6 times the density of water.

A

11.696 m

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B

10.696 m

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C

11.423 m

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D

12.696 m

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Solution

The correct option is A 11.696 m Given: Height of mercury column, h1 =0.86 m Let h2 be the height of water column which will produce the same pressure as height h1 of the mercury column. ρ1 and ρ2 are densities of mercury and water respectively. Weight =W mass =m Volume =V Acceleration due to gravity=g Weight of water must equal to the weight of mercury in the column. Wwater=Wmercury mwaterg=mmercuryg ρ2Vwaterg=ρ1Vmercuryg ρ2Ah2g=ρ1Ah1g h2 = h1ρ1ρ2 Given, ρ1=13.6×ρ2 ρ1ρ2=13.6 Hence, h2=13.6×0.86=11.696 m.

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