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Calculate the force exerted per unit of area by a column of mercury (density 5 13.59 g/cm3) that is 76.0 cm high. How high would a column of water (density 5 1.00 g/cm3) have to be to exert the same force

Respuesta :

Answer:

Part A

[tex]1.01 * 10^5 Pa[/tex]

Part B

[tex]10.3[/tex] meters

Step-by-step explanation:

Part A

Density of mercury is [tex]13.59[/tex] gram per centimeter cube

Volume of the  column of mercury when are is assumed to be unit

[tex]76 * 1* 1\\=76[/tex]

We know that mass is the product of density and volume.

Thus mass of this column of mercury is equal to

[tex]76 * 13.59\\= 1032.84[/tex]

Or [tex]1.03[/tex] Kilograms

Force is equal to

[tex]mg\\= 1.03 * 9.81\\= 10.1 \frac{Kgm}{s^2} \\= 10.1 N[/tex]

Pressure or force per unit area

[tex]\frac{10.1 * 100* 100}{1} \\= 1.01 * 10^5 \frac{N}{m^2} \\= 1.01 * 10^5 Pa[/tex]

Part B

Height of the column

[tex]76 * 13.59\\1032. 84 cm\\10.32 m[/tex]

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