If the normal atmospheric pressure in a laboratory supports a column of mercury 0.76m high and the relative density of mercury is 13.8, then the height of water column which atmospheric pressure will support in the same laboratory at the same time is

Truss

1 year ago

To determine the height of the water column that atmospheric pressure will support, we use the principle that the pressure exerted by a liquid column is given by:

P = h \rho g

where:

is the pressure,

is the height of the liquid column,

is the density of the liquid,

is the acceleration due to gravity.


Since the atmospheric pressure remains the same for both mercury and water, we set the pressure exerted by the mercury column equal to the pressure exerted by the water column:

h_{\text{Hg}} \times \rho_{\text{Hg}} \times g = h_{\text{H₂O}} \times \rho_{\text{H₂O}} \times g

Canceling from both sides:

h_{\text{Hg}} \times \rho_{\text{Hg}} = h_{\text{H₂O}} \times \rho_{\text{H₂O}}

Given:

m,

(since relative density of mercury is 13.8),

(assuming water's relative density is 1).


Solving for :

h_{\text{H₂O}} = \frac{h_{\text{Hg}} \times \rho_{\text{Hg}}}{\rho_{\text{H₂O}}}

h_{\text{H₂O}} = \frac{0.76 \times 13.8}{1}

h_{\text{H₂O}} = 10.488 \approx 10 \text{ m}

Thus, the correct answer is:

B. 10m.

🤍FROST🤍

3 months ago

I got some answers correctly but in the correction and markings I missed them

🤍FROST🤍

3 months ago

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