A) same as that of B
B) opposite to that of B
C) \[\theta ={{\tan }^{-1}}\left( \frac{1}{2} \right)\]to the x-axis
D) \[\theta ={{\tan }^{-1}}\left( \frac{-1}{2} \right)\]
Correct Answer: C
Solution :
Here, \[{{\mathbf{p}}_{i}}={{m}_{2}}v\mathbf{i}+{{m}_{2}}\times 0\] \[{{\mathbf{p}}_{f}}={{m}_{2}}\frac{v}{2}\mathbf{j}+{{m}_{1}}\times {{v}_{2}}\] Law of conservation of momentum \[{{\mathbf{p}}_{i}}={{\mathbf{p}}_{f}}\] \[{{m}_{2}}v\mathbf{i}={{m}_{2}}\frac{v}{2}\mathbf{j}+{{m}_{2}}\times {{v}_{1}}\] \[{{v}_{1}}=\frac{{{m}_{2}}}{{{m}_{1}}}v\mathbf{i}+\frac{{{m}_{2}}}{{{m}_{1}}}\frac{v}{2}\mathbf{j}\] From this equation we can find\[\tan \theta =\frac{1}{2}\] \[\theta ={{\tan }^{-1}}\left( \frac{1}{2} \right)\]to the x-axis.You need to login to perform this action.
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