A) 100 \[m{{s}^{-1}}\]
B) \[80\,m{{s}^{-1}}\]
C) \[40\,m{{s}^{-1}}\]
D) \[120\,m{{s}^{-1}}\]
Correct Answer: A
Solution :
Key Idea: In the given problem conservation of linear momentum and energy hold good. Conservation of momentum yields. \[{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}=0\]or\[4{{v}_{1}}+0.2{{v}_{2}}=0\] ...(i) Conservation of energy yields \[\frac{1}{2}{{m}_{1}}v_{1}^{2}+\frac{1}{2}{{m}_{2}}v_{2}^{2}=1050\] or\[\frac{1}{2}\times 4v_{1}^{2}+\frac{1}{2}\times 0.2\times v_{2}^{2}=1050\] or\[2v_{1}^{2}+0.1v_{2}^{2}=1050\] ...(ii) Solving Eqs. (i) and (ii), we have \[{{v}_{1}}=100\,m/s\]
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