Question

A person presses the earth least when he is:
A). Sitting
B). Standing
C). Running
D). Laying on the ground

Answer 1

Hint: Think of why it is more comfortable to sleep on a mattress than on bare floor in terms of pressure exerted and the area of contact between your body and the mattress. How would you justify being able to lie flat on sand without sinking whereas standing on your feet would make you sink faster? Is it just your weight, or your area of contact, or both? This is also the same reason why the person would “press” the earth least in this state of being.

Formula Used:
Pressure exerted $P = \dfrac{F}{A}$, where F is the force exerted and A is the area over which this force is exerted.

Complete step-by-step solution:
Let us begin by translating the term “press” into something that is more physically familiar to us. This is nothing but an exertion of pressure.
Now, we know that the pressure exerted by body on a surface, which can also be defined as the force exerted by a body per unit area can be given as:
$P = \dfrac{F}{A}$
From the above relation, we can establish that pressure exerted on a body and its area of contact follow an inverse relation. And the pressure applied on a body is directly proportional to the force exerted on the body.
Therefore, more pressure = more force and less contact area, and less pressure = less force and more contact area.
Now let us look at this relation in the context of our question.
Here, the exerted force will be the person’s weight, which is directly proportional to the pressure exerted.
It is pretty straightforward to infer that when the person in sitting or standing in comparison to lying flat on the ground, the area of contact between the person’s body is much less and thus, he presses the ground more than he would if he was laying on the ground, where his weight would get distributed over the large surface area of the ground that his body would occupy.
Similarly, when the man is running, he is constantly exerting his weight on the ground to get enough normal reaction to launch his feet, facilitating his motion. Since he is applying a lot of his weight via his feet onto the ground, and his feet also have a lesser surface area compared to when he’s laying on the ground, this leads to him exerting a relatively higher pressure on the ground.
Therefore, he exerts the least pressure on the ground when he is laying on the ground.
To this end, the correct option would be (D). Laying on the ground

Note: Remember that the magnitude of pressure depends on the “area of contact” with the object and not just the geometric area of the object. This is evident from the basis of our inference, in our justification above, as the area of contact between the person and the earth is in the increasing order of standing, sitting and lying on the ground, and hence lying on the ground exerts less pressure than the other positions. Also, the force exerted contributes to the pressure incident on the object, as was the case when the person was running.
But do not forget that less area of contact is not always the desirable thing! For example, a sharp knife has a lesser surface area but cuts better than a blunt knife. This is because the sharp knife exerts more pressure on the object due to less area of contact between them. However, the area of contact between a blunt knife and the object is larger and the weight(pressure) that we exert on the knife will get evened out over this area and will be less impacting.