एक व्यक्ति का भार 80 kg है। उसके द्वारा जमीन पर कितना दाब लगाया जायेगा, जब (i) वह लेटाने पर (ii) वह अपने पैरों पर खड़ा है? दिया है: व्यक्ति के शरीर का क्षेत्रफल 1.2 m² तथा एक पैर का 60 cm² (g = 9.8 ms⁻²)

Step-by-step solution

1. 1

   Given Data

   Mass $m = 80 \text{ kg}$, $g = 9.8 \text{ m/s}^2$

   $$m = 80 \text{ kg}, g = 9.8 \text{ m/s}^2$$
2. 2

   Pressure Formula

   Pressure is Force per unit Area: $P = F/A$

   $$P = \frac{F}{A}$$
3. 3

   Calculate Force

   Force exerted by the person is their weight: $F = mg$

   $$F = mg$$
4. 4

   Calculate Weight

   Substitute values: $F = 80 \text{ kg} \times 9.8 \text{ m/s}^2$

   $$F = 80 \times 9.8 \text{ N}$$
5. 5

   Weight Value

   The force (weight) is $F = 784 \text{ N}$

   $$F = 784 \text{ N}$$
6. 6

   Case (i): Lying Down

   Area $A_1 = 1.2 \text{ m}^2$. Pressure $P_1 = F/A_1$

   $$P_1 = \frac{784 \text{ N}}{1.2 \text{ m}^2}$$
7. 7

   Pressure (i) Result

   Pressure $P_1 = 653.33 \text{ Pa}$

   $$P_1 = 653.33 \text{ Pa}$$
8. 8

   Case (ii): Standing

   Area of one foot $= 60 \text{ cm}^2 = 60 \times 10^{-4} \text{ m}^2$

   $$A_{\text{foot}} = 60 \text{ cm}^2 = 60 \times 10^{-4} \text{ m}^2$$
9. 9

   Total Standing Area

   Total area $A_2 = 2 \times 60 \times 10^{-4} \text{ m}^2 = 120 \times 10^{-4} \text{ m}^2 = 0.012 \text{ m}^2$

   $$A_2 = 2 \times 60 \times 10^{-4} \text{ m}^2 = 0.012 \text{ m}^2$$
10. 10

    Pressure (ii) Calculation

    Pressure $P_2 = F/A_2 = 784 \text{ N} / 0.012 \text{ m}^2$

    $$P_2 = \frac{784 \text{ N}}{0.012 \text{ m}^2}$$