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.

Explanation:

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

               P = $\rho \times g \times h$

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

     $\rho_{Hg} \times g \times h_{Hg} =\rho_{H_{2}O} \times g \times h_{H_{2}O}$

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

         $\rho_{Hg} \times g \times h_{Hg} =\rho_{H_{2}O} \times g \times h_{H_{2}O}$

       $13.6 g/cm^{3} \times 256 mm = 1 \times h_{H_{2}O}$

            3481.6 mm = $h_{H_{2}O}$

As 1 mm = 0.1 cm

            $3481.6 mm \times \frac{0.1 cm}{1 mm}$

            = 348.1 cm

or,        = 348 cm (approx)

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