question_answer

A body is moving in a starting line with certain velocity. Another body with double the mass and half the velocity of the first, is moving in the straight line. What is the ratio of kinetic energy of 2nd body with the first body?

Answer:

\[{{1}^{st}}\,\,body=K{{E}_{1}}\frac{1}{2}m{{v}^{2}}\] \[{{2}^{nd}}\,\,body=K{{E}_{2}}=\frac{1}{2}(2m){{\left( \frac{V}{2} \right)}^{2}}\]                                                 \[=\frac{1}{2}2m\times \frac{{{V}^{2}}}{4}\]                                                 \[\frac{1}{2}m{{v}^{2}}\times \frac{1}{2}\] \[\Rightarrow K{{E}_{2}}=\frac{K{{E}_{1}}}{2}\]