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The gravitational force exerted by an object is given by F 5 mg where F is the force in newtons, m is the mass in kilograms, and g is the acceleration due to gravity, 9.81 m/s². 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]P = 1.013 \times 10^5 Pa[/tex]

Part b)

[tex]H = 10.3 m[/tex]

Explanation:

As we know that force due to gravity is given as

[tex]F = mg[/tex]

now for force per unit area is given as

[tex]P = \frac{F}{A}[/tex]

[tex]P = \frac{\rho Ah g}{A}[/tex]

[tex]P = \rho g H[/tex]

so for mercury we will have

[tex]P = (13.59 \times 10^3) (9.81)(0.76)[/tex]

[tex]P = 1.013 \times 10^5 Pa[/tex]

Part b)

Now if water also apply same force per unit area

then we will have

[tex]P = \rho g H[/tex]

[tex]1.013 \times 10^5 = (1000) 9.81 H[/tex]

[tex]H = 10.3 m[/tex]

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