A) \[\frac{200}{3}J\]
B) \[\frac{500}{3}J\]
C) \[\frac{400}{3}J\]
D) \[\frac{800}{3}J\]
Correct Answer: C
Solution :
\[{{v}_{CM}}=\frac{{{m}_{1}}\frac{d{{r}_{1}}}{dt}+{{m}_{2}}\frac{d{{r}_{2}}}{dt}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{4\times 5\,\hat{i}+2\times 10\,\hat{i}}{4+2}\] \[{{v}_{CM}}=\frac{40\,\hat{i}}{6}=\frac{20\,\hat{i}}{3}\] The kinetic energy \[K=\frac{1}{2}m{{v}^{2}}\] \[=\frac{1}{2}\times (4+2)\times \frac{20\times 20}{3\times 3}\] \[=\frac{1}{2}\times \frac{6\times 20\times 20}{3\times 3}\] \[K=\frac{400}{3}J\]
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