A) \[3\hat{i}-1.5\hat{j}\,m{{s}^{-1}}\]
B) \[60\hat{i}-30\hat{j}\,m{{s}^{-1}}\]
C) \[20\hat{i}-3\hat{j}\,m{{s}^{-1}}\]
D) \[23\hat{i}-1.5\hat{j}\,m{{s}^{-1}}\]
Correct Answer: D
Solution :
| Initial velocity of centre of mass is |
| \[u=\frac{{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] |
| \[=\frac{3\,(2\hat{i}+3\hat{j})+3\,(4\hat{i}-6\hat{j})}{3+3}=3\hat{i}-1.5\hat{j}m{{s}^{-1}}\] |
| Acceleration of centre of mass is |
| \[a=\frac{F}{{{m}_{\text{system}}}}=\frac{24\hat{i}}{3+3}=4\hat{i}\,m{{s}^{-\,2}}\] |
| Final velocity of centre of mass is |
| \[v=u+at\] |
| \[=(3\hat{i}+1.5\hat{j})+(4\hat{i}\times 5)=23\hat{i}-1.5\hat{j}\,m{{s}^{-1}}\] |
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