An elephant, whose mass is 5000 kg, stands on his two back feet. If the diameter of the elephant's foot is 16 cm, the pressure exerted by the elephant on the ground is
A) 1.2 MPa.
B) 1.8 MPa.
C) 2.4 MPa.
D) 3.0 MPa.

Question

Quizplus · Accepted Answer

The pressure exerted by the elephant can be calculated using the formula $P = \frac{F}{A}$, where $P$ is the pressure, $F$ is the force (in this case, the weight of the elephant), and $A$ is the area over which the force is distributed. The force due to gravity (weight) is $F = mg$, where $m$ is the mass of the elephant (5000 kg) and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). The area of one foot is given by the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the foot. Since the elephant stands on two feet, the total area is twice the area of one foot.Given:- $m = 5000 \, \text{kg}$- $g = 9.8 \, \text{m/s}^2$- Diameter of the foot = 16 cm = 0.16 m, so the radius $r = 0.08 \, \text{m}$First, calculate the force (weight):$$F = mg = 5000 \times 9.8 = 49000 \, \text{N}$$Then, calculate the area of one foot:$$A_{\text{one foot}} = \pi r^2 = \pi \times (0.08)^2 = \pi \times 0.0064 \, \text{m}^2$$The total area for two feet is:$$A_{\text{total}} = 2 \times A_{\text{one foot}} = 2 \times \pi \times 0.0064 \, \text{m}^2$$Finally, calculate the pressure:$$P = \frac{F}{A_{\text{total}}} = \frac{49000}{2 \times \pi \times 0.0064} \, \text{N/m}^2$$Plugging in the values:$$P \approx \frac{49000}{0.040212385} \approx 1218379.53 \, \text{N/m}^2 = 1.2 \, \text{MPa}$$Therefore, the pressure exerted by the elephant on the ground is approximately 1.2 MPa.

An Elephant, Whose Mass Is 5000 Kg, Stands on His