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Question: At sea level, the atmospheric pressure is \(1.04 \times {10^5}\,Pa\). Assuming \(g = 10m{s^{ - 2}}\)...

At sea level, the atmospheric pressure is 1.04×105 Pa1.04 \times {10^5}\,Pa. Assuming g=10ms−2g = 10m{s^{ - 2}} and density of air to be uniform and equal to 1.3 kgm−31.3\,kg{m^{ - 3}}, find the height of the atmosphere.
A. 8000 km8000\,km
B. 8000 mm8000\,mm
C. 8000 cm8000\,cm
D. 8000 m8000\,m

Explanation

Solution

we will use the formula used for calculating the atmospheric pressure. Then, we will put the values of atmospheric pressure, ρ\rho density of the air and gg acceleration due to gravity in the formula of atmospheric pressure. The value of atmospheric pressure is t sea level and we will calculate the height of the atmosphere by using the following given formula of the pressure.

Formula used:
The formula used for calculating the atmospheric pressure is given below
P=hρgP = h\rho g
Here, PP is the atmospheric pressure, hh is the height of the atmosphere, ρ\rho is the density of the air and gg is the acceleration due to gravity.

Complete step by step answer:
Here, the atmospheric pressure at the sea level is P=1.04×105 PaP = 1.04 \times {10^5}\,Pa
Also, the density of air, ρ=1.3 kgm−3\rho = 1.3\,kg{m^{ - 3}}
The acceleration due to gravity is g=10ms−2g = 10m{s^{ - 2}}
The formula used for calculating the atmospheric pressure is given below
P=hρgP = h\rho g
Here, PP is the atmospheric pressure, hh is the height of the atmosphere, ρ\rho is the density of the air and gg is the gravitational acceleration.
Now, the height of the atmosphere can be calculated as shown below
⇒ h=Pρg\Rightarrow \,h = \dfrac{P}{{\rho g}}
Now, putting the values of atmospheric pressure, ρ\rho density of the air and gg acceleration due to gravity in the above equation to calculate the height of the atmosphere as shown below
h=1.04×1051.3×10h = \dfrac{{1.04 \times {{10}^5}}}{{1.3 \times 10}}
⇒ h=1.04×10513\Rightarrow \,h = \dfrac{{1.04 \times {{10}^5}}}{{13}}
⇒ h=0.08×105\Rightarrow \,h = 0.08 \times {10^5}
∴ h=8000 m\therefore \,h = 8000\,m
Therefore, the height of the atmosphere is 8000 m8000\,m.

Hence, option D is the correct option.

Note: We have not changed the units of the terms given in the question because all the units given in the question are bigger units. The height of the pressure comes out to be in meters by solving the question. If we will change the units then the answer will not come out to be the same.