question_answer

A light body and a heavy body have the same momentum. Which one will have greater kinetic energy?       Or                      Two bodies of unequal masses have same linear momentum, which one has greater kinetic energy?                                     

Answer:

                Kinetic energy, \[K=\frac{1}{2}m{{\upsilon }^{2}}=\frac{{{(m\upsilon )}^{2}}}{2m}=\frac{{{p}^{2}}}{2m}\]                 For constant p, \[K\propto \frac{1}{m}\] Thus the lighter body has more kinetic energy than the heavier body.