The air pressure at sea level is about 0.1 MPa or 101000 Pa.
The pressure is given as,
[tex]P=\frac{F}{A}[/tex]Rearranging the above equation in order to get an expression for force,
[tex]F=PA[/tex]For the cossestion area of 1 square centimeter, the force is given as,
[tex]\begin{gathered} F=101000\text{ Pa}\times(1\text{ cm})^2 \\ =101000\text{ Pa}\times(0.01\text{ m})^2 \\ =101000\text{ Pa}\times0.0001m^2 \\ =10.1\text{ N} \end{gathered}[/tex]The force is give as,
[tex]\begin{gathered} F=ma \\ =mg \end{gathered}[/tex]Here, g is the acceleration due to gravity .
Rearranging the above equation in order to get mass,
[tex]m=\frac{F}{g}[/tex]Substituting all known values,
[tex]\begin{gathered} m=\frac{10.1\text{ N}}{(10ms^{-2})^{}} \\ =1.01\text{ kg} \\ \cong1\text{ kg} \end{gathered}[/tex]Therefore, the appropriate mass of 1 square centimeter column of air that extends from sea level to the top of atmosphere is 1 kg. Hence, option (b), is the correct choice.
