A) \[-24\,\,m\,\,{{s}^{-1}}\]towards west
B) \[14\,\,m\,\,{{s}^{-1}}\]towards east
C) \[24\,\,m\,\,{{s}^{-1}}\]towards north
D) \[54\,\,m\,\,{{s}^{-1}}\]towards south
Correct Answer: A
Solution :
According to the law of conservation of linear momentum,\[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}+{{v}_{1}}+{{m}_{2}}{{v}_{2}}\] \[\Rightarrow \]\[0={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}},\,\,0=0.2\times 12+0.1\times {{v}_{2}}\] \[\Rightarrow \] \[{{v}_{2}}=\frac{-0.2\times 12}{0.1}=-24\,\,m\,\,{{s}^{-1}}\] The negative sign indicates that it is moving in the opposite direction (west) with a velocity of\[-24\,\,m\,\,{{s}^{-1}}\].
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