A mercury barometer reads 76 cm. What will be reading on a barometer filled with water at the same place? Mercury is 13.6 denser than water.  

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The pressure is determined as the product of liquid density (`rho` ), acceleration due to gravity (g) and height of the liquid column (h), as:

Pressure = `rhogh`

Now, assuming the density of water to be 1 gm/cm^3 (or 1000 km/m^3), acceleration due to gravity as 10 m/s^2, we can calculate...

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The pressure is determined as the product of liquid density (`rho` ), acceleration due to gravity (g) and height of the liquid column (h), as:

Pressure = `rhogh`

Now, assuming the density of water to be 1 gm/cm^3 (or 1000 km/m^3), acceleration due to gravity as 10 m/s^2, we can calculate the pressure, when mercury (density = 13.6 gm/cm^3 or 13600 kg/m^3) is the desired fluid, as: 

Pressure = 13600 kg/m^3 x 10 m/s^2 x 0.76 m

The same pressure can be measured by a water based barometer and the height of water column can be determined as:

Pressure = 1000 kg/m^3 x 10 m/s^2 x h = 13600 kg/m^3 x 10 m/s^2 x 0.76 m

Hence, we can see that water column will have 13.6 times the height of the mercury column and this water column have to be as high as 1033.6 cm or 10.34 m

Conversely, a water barometer will read only 1/13.6 th pressure for the same height of the liquid column. 

Hope this helps. 

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