Understanding Pressure and Contact Area

The question asks when the pressure exerted by a man on the earth is minimum. Pressure is defined as the force applied per unit area. Mathematically, it is given by:

$$P = \frac{F}{A}$$

where:

• \(P\) is the pressure.
• \(F\) is the force applied.
• \(A\) is the area over which the force is applied.

In this case, the force exerted by the man on the earth is his weight, which is constant regardless of his posture. Therefore, to minimize the pressure (\(P\)), the area of contact (\(A\)) between the man and the earth must be maximized.

Analyzing Contact Area in Different Postures

Let's examine the contact area in each of the given postures:

1. Stands on his feet: When a man stands on his feet, the contact area is the area of the soles of both feet touching the ground.
2. Sits with folded legs: When a man sits with folded legs, the contact area includes the area of the buttocks and potentially parts of the legs or feet touching the ground. This area is larger than the soles of the feet.
3. Sleeps on the ground: When a man sleeps on the ground (either on his back or front), the contact area is the entire surface of his body that is in contact with the ground. This is significantly larger than standing or sitting areas.
4. Stands on one foot: When a man stands on one foot, the contact area is the area of the sole of just one foot. This is the smallest contact area among all options.

We can compare the approximate contact areas for each posture:

Determining Minimum Pressure

Since pressure is inversely proportional to the area of contact for a constant force (weight), the pressure exerted will be minimum when the area of contact is maximum. From our analysis, sleeping on the ground provides the largest contact area.

Therefore, the pressure exerted by the man on the earth is minimum when he sleeps on the ground.