Question

A pressure that will support a column of Hg to a height of 256mm would support a column of water to what height? The density of mercury is 13.6 g/cm3; the density of water is 1.00g/cm3.

A. 348cm
B. 1.00 ´ 102 ft
C. 18.8mm
D. 33.8ft
E. 76.0 cm

Answer 1

Answer: Option (A) is the correct answer.

Step-by-step explanation:

It is known that relation between pressure, density, height, and gravity is as follows.

P =
`\rho * g * h`

As it is given that pressure of both mercury and water column are equal. Therefore,

`\rho_(Hg) * g * h_(Hg) =\rho_{H_(2)O} * g * h_{H_(2)O}`

Cancelling the common terms in the formula. Now, putting the given values into the above formula as follows.

`\rho_(Hg) * g * h_(Hg) =\rho_{H_(2)O} * g * h_{H_(2)O}`

`13.6 g/cm^(3) * 256 mm = 1 * h_{H_(2)O}`

3481.6 mm =
`h_{H_(2)O}`

As 1 mm = 0.1 cm

`3481.6 mm * (0.1 cm)/(1 mm)`

= 348.1 cm

or, = 348 cm (approx)

thus, we can conclude that height of the given column is 348 cm.