Answer:
(a) We know that \[Pressure=\frac{Force}{Area}\] Atmospheric pressure is the force exerted by an air column of\[1{{m}^{2}}\] cross-sectional area on the ground. The force exerted by the air column is nothing but its weight. \[\therefore \]Force exerted by the air column = weight of air column = mass of air column × acceleration due to gravity = mg The mass of air column of\[1{{m}^{2}}\] cross sectional is approximately\[{{10}^{4}}kg\] and acceleration due to gravity is\[9.8\text{ }m/{{s}^{2}}\approx 10m/{{s}^{2}}\]. \[\therefore \]Atmospheric pressure \[=\frac{Force}{Area}=\frac{m\times g}{1}=\frac{{{10}^{4}}\times 10}{1}N/{{m}^{2}}={{10}^{5}}N/{{m}^{2}}\] \[={{10}^{5}}\text{ }pascal\] So, atmospheric pressure is \[{{10}^{5}}N/{{m}^{2}}.\] This means that on an area of\[1{{m}^{2}}\]of the surface of earth, a force of \[{{10}^{5}}\] Newton is acting. This is equivalent to the weight of 140 adults of mass, 70 kg each. This is also approximately the weight of a body of mass, ten tonnes (10,000 kg). This is also equal to the weight of two elephants, approximately. (b) Considering the head as a sphere with an average diameter of 20cm the resulting surface area is about\[1256\,c{{m}^{2}}\]. We know that for every one \[c{{m}^{2}}\] of area a force of approximately 10 Newton acts due to atmospheric pressure. Therefore the total force of about 1256 10N acts on our head which is equal to the weight of 18 adults weighing 70 kg each.
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