Question

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?

Answer 1

Part a)

`P = 1.013 * 10^5 Pa`

Part b)

`H = 10.3 m`

Step-by-step explanation:

As we know that force due to gravity is given as

`F = mg`

now for force per unit area is given as

`P = (F)/(A)`

`P = (\rho Ah g)/(A)`

`P = \rho g H`

so for mercury we will have

`P = (13.59 * 10^3) (9.81)(0.76)`

`P = 1.013 * 10^5 Pa`

Part b)

Now if water also apply same force per unit area

then we will have

`P = \rho g H`

`1.013 * 10^5 = (1000) 9.81 H`

`H = 10.3 m`