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The gravitational force exerted by an object is given by F= mg where F is the force in newtons, m is the mass in kilograms, and g is the acceleration due to gravity, 9.81m/s2. Calculate the force exerted per unit of area by a column of mercury (density =13.59g/cm3) that is 76.0cm high. How high would a column of water (density =1.00g/cm3) have to be to exert the same force?

Sagot :

The force exerted per unit of area by a column of mercury is 1.01×10⁵ Pa and height of column that will exert same force is 10.3 m.

We will be using the formula mentioned below for both the calculations.

P = rho×g×h, where P is pressure, rho is density, g is acceleration due to gravity and h is height.

Firstly converting the units to m and kg.

Height = 76 cm

100 cm = 1 m

So, height = 0.76 m

Density = 13.59×(10²)³/10³

Density = 13590 kg/m³

Keep the value in formula for calculation pressure, which is force per unit area

Pressure = 13590×9.81×0.76

Performing multiplication

Pressure = 1.01×10⁵ Pa

Now finding height of column in case same force and liqui being water

Calculating density = 1×(10²)³/10³

Density = 1×10³ kg/m³

h = P/rho×g

h = 1.01×10⁵/(9.81×10³)

Performing division

height = 10.3 m

Hence, pressure is 1.01×10⁵ Pa and height is 10.3 m.

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