A) \[\frac{4}{9}\]
B) \[\frac{5}{9}\]
C) \[\frac{1}{9}\]
D) \[\frac{8}{9}\]
Correct Answer: D
Solution :
| [d] \[{{v}_{2}}=\frac{{{m}_{1}}+{{u}_{1}}+{{u}_{2}}({{m}_{2}}-{{m}_{1}})}{{{m}_{1}}+{{m}_{2}}}\] |
| \[{{v}_{2}}=\frac{2(4m)u+0}{6m}\] |
| \[{{v}_{2}}=\frac{4}{3}u\] |
| \[\frac{\Delta E}{E}=\frac{\frac{1}{2}2mv_{2}^{2}}{\frac{1}{2}4m{{u}^{2}}}=\frac{{{\left( \frac{4}{3}u \right)}^{2}}}{2{{u}^{2}}}=\frac{8}{9}\] |
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