A) 2v
B) v/\[\sqrt{2}\]
C) v/2
D) \[\sqrt{2}\]v
Correct Answer: B
Solution :
Let the speed of the third part be \[{{v}_{3}}.\] Applying the law of conservation of momentum, we have \[\sqrt{p_{1}^{2}+p_{2}^{2}}=p\] \[\Rightarrow \] \[p_{1}^{2}+p_{2}^{2}={{p}^{2}}\] \[\therefore \] \[{{({{m}_{1}}{{v}_{1}})}^{2}}+{{({{m}_{2}}{{v}_{2}})}^{2}}={{({{m}_{3}}{{v}_{3}})}^{2}}\] \[\Rightarrow \] \[{{(m\times v)}^{2}}+{{(m\times v)}^{2}}={{(2m\times {{v}_{3}})}^{2}}\] \[\Rightarrow \] \[{{m}^{2}}{{v}^{2}}+{{m}^{2}}{{v}^{2}}=4{{m}^{2}}v_{3}^{2}\] \[\Rightarrow \] \[2{{m}^{2}}{{v}^{2}}=4{{m}^{2}}v_{m}^{2}\] \[\Rightarrow \] \[{{v}_{3}}=\frac{v}{\sqrt{2}}\]
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