question_answer

Who exerts more pressure? (a)    A girl of 50 kg wearing heels with an area of cross section\[1\text{ }c{{m}^{2}}\]. (b)   An elephant of 4000 kg with foot area of each \[250\text{ }c{{m}^{2}}.\]

Answer:

(a) Girl Mass \[(m)=50\text{ }kg\] Area of a heel \[(a)=1c{{m}^{2}}\] Area of two heels \[(A)=2\times 1c{{m}^{2}}=2c{{m}^{2}}\] \[=2\times {{10}^{4}}{{m}^{2}}\] Force \[(F)=mg=50\times 10=500\text{ }N\] Pressure exerted by the girl \[\frac{F}{A}=\frac{500}{2\times {{10}^{-4}}}=250\times {{10}^{4}}Pa\] (b) Elephant Mass \[(m)=4000\text{ }kg\] Area of one leg \[=250c{{m}^{2}}\] Area of four feet \[(A)=4\times 250\text{ }c{{m}^{2}}\] \[=1000\text{ }c{{m}^{2}}=1000\times {{10}^{4}}{{m}^{2}}=0.1{{m}^{2}}\] Force \[(F)=mg=4000\times 10=4000\text{ }N\] Pressure exerted by the elephant \[\frac{F}{A}=\frac{2000}{0.1}=20\times {{10}^{4}}Pa\] It is clear that the girl is exerting more pressure on the ground than that of the elephant.