Question

(1) Calculate the height of a water column which will exert on its base the same pressure as the 70 cm column of mercury. Density of mercury is 13.6 g cm^-3.
(2)Will the height of the water column in part (a) change if the cross section of the water column is made wider ?
[Ans.] (1) 9.52 m (b) No
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Answer 1

Dear Student,

If the columns have to exert the same pressure (P) = F/A on the same area, they need to have the same F.

F will be the weight of the columns.

Now, we know

Density = Mass / Volume

Mass = Volume x Density

Now volume = area of base x Height = A x H

It is given that area is same

Mass = A x H x Density

Weight = M g

Now

Weight of water column = Weight of mercury column

A x H_water x Density_water x g = A x H_Mercury x Density_Mercury x g

H_water= H_Mercury x Density_Mercury / Density_water

= 70 cm x 13.6 g/cc / 1 = 952 cm

No because pressure depends upon just height and fluid density.