question_answer

The foot of an elephant has an area of\[275\text{ }c{{m}^{2}}\]. If the mass of the elephant is 2200 kg, find the pressure exerted by the elephant on the ground. ( \[g=10m{{s}^{-2}}\]).          

Answer:

                     Area of one foot\[=275\text{ }c{{m}^{2}}\] \[=275\times {{10}^{4}}{{m}^{2}}\]          \[(\because 1c{{m}^{2}}={{10}^{4}}{{m}^{2}})\] But total force is acting through the four legs. So, total area of the four feet (A) \[=4\times 275\times {{10}^{4}}{{m}^{2}}\] Mass of the elephant \[(m)=2200\text{ }kg\] \[g=10\text{ }m{{s}^{2}}\] Pressure exerted (P) = ? We know, pressure\[(P)=\frac{Force\text{ }exerted}{Area}\] Force exerted by the elephant is equal to weight of the elephant. \[P=\frac{mg}{A}\]                          \[(\because F=W=mg)\] Substituting the values in the above equation, we get, \[P=\frac{2200\times 10}{4\times 275\times {{10}^{-4}}}=\frac{22\times {{10}^{3}}\times {{10}^{4}}}{1100}=\frac{22\times {{10}^{7}}}{11\times {{10}^{2}}}\] \[P=2\times {{10}^{5}}Pa\] Therefore, pressure exerted by the elephant is \[2\times {{10}^{5}}Pa.\]