A) \[300%\]
B) \[150%\]
C) \[75%\]
D) \[200%\]
Correct Answer: A
Solution :
Initial momentum\[{{p}_{1}}=100\,\,p\] Final momentum\[{{p}_{2}}=200\,\,p\] Initial kinetic energy\[{{K}_{1}}=K\] The kinetic energy is given by \[K=\frac{{{p}^{2}}}{2m}\propto {{p}^{2}}\] or\[\frac{{{K}_{1}}}{{{K}_{2}}}={{\left( \frac{{{p}_{1}}}{{{p}_{2}}} \right)}^{2}}\]or\[\frac{{{K}_{1}}}{{{K}_{2}}}={{\left( \frac{100p}{200p} \right)}^{2}}=\frac{1}{4}\] \[{{K}_{2}}=4\,\,{{K}_{1}}\] Increase in kinetic energy is \[=4{{K}_{1}}-{{K}_{1}}=3{{K}_{1}}=300%\]
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