A) \[\frac{1}{2}\] of its initial kinetic energy
B) \[\frac{1}{9}\] of its initial kinetic energy
C) \[\frac{8}{9}\] of its initial kinetic energy
D) \[\frac{1}{4}\]of its initial kinetic energy
Correct Answer: C
Solution :
\[\frac{\Delta K}{K}=\left[ 1-{{\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)}^{2}} \right]=\left[ 1-{{\left( \frac{m-2m}{m+2m} \right)}^{2}} \right]\]\[=\frac{8}{9}\] \[\Delta K\]=\[\frac{8}{9}K\]i.e. loss of kinetic energy of the colliding body is \[\frac{8}{9}\] of its initial kinetic energy.
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