Question

At sea level, the atmospheric pressure is $1.04 \times {10^5}\,Pa$. Assuming $g = 10m{s^{ - 2}}$ and density of air to be uniform and equal to $1.3\,kg{m^{ - 3}}$, find the height of the atmosphere.
A. $8000\,km$
B. $8000\,mm$
C. $8000\,cm$
D. $8000\,m$

Answer 1

Hint:we will use the formula used for calculating the atmospheric pressure. Then, we will put the values of atmospheric pressure, $\rho $ density of the air and $g$ 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
$P = h\rho g$
Here, $P$ is the atmospheric pressure, $h$ is the height of the atmosphere, $\rho $ is the density of the air and $g$ is the acceleration due to gravity.

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

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.