Question

Calculate the height of the 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/$cm^3$.
A. 850 cm
B. 952 cm
C. 760 cm
D. 560 cm

Answer 1

We all know that at the common base point the pressure is the same. Here we will firstly find the hydrostatic pressure due to the mercury column and then we will equate it with the pressure of the water column so that we can get the height appropriately.

Complete Solution
Given:
The height of the mercury column is h=70 cm.
The density of mercury is d=13.6g/$cm^3$.
We will now calculate the pressure ${P_{Hg}} = hdg$ due to the mercury column.
We will now substitute h=70 cm, d=13.6gcm-3, to find the value of ${P_{Hg}}$.
${P_{Hg}} = 70\;{\rm{cm}} \times 13.6{\rm{g/c}}{{\rm{m}}^3} \times g$
We know that pressure due to the water column is ${P_w} = {h_w}{d_w}g$.
Here, hw is the height of the water column, and dw = 1 g/$cm^3$ is the density of the water column and g is the acceleration due to gravity.
We will now equate ${P_w}$ and ${P_{Hg}}$ to find the value of height $h_w$.
${P_w} = {P_{Hg}}$
$\Rightarrow {h_w} \times 1{\rm{g/c}}{{\rm{m}}^3} \times g = 70\;{\rm{cm}} \times 13.6\;{\rm{g/c}}{{\rm{m}}^3} \times g$
$\Rightarrow {h_w} = 952\;{\rm{cm}}$
Therefore, the height of the water column which will exert on its base the same pressure as the 70 cm column of mercury is 952 cm.

the correct option is (B).

Note: We know that pressure is a scalar quantity defined as force applied per unit area and the force should be perpendicular to the area. But fluid pressure is the measure of force per unit area of an object in a closed container or in a fluid. According to Pascal’s law the pressure applied on a fluid will be transmitted throughout the fluid and to the walls of the container without any change in the magnitude of the pressure. We must keep in mind that we must take care of the units whether we are applying the C.G.S system or the M.K.S system.