A) \[\frac{2V}{3}\]
B) \[2V\]
C) \[\frac{V}{2}\]
D) \[V\]
Correct Answer: C
Solution :
\[{{F}_{ext}}=0,\]since \[{{a}_{CM}}=0\] \[\vec{p}={{\rho }_{A}}+{{\rho }_{B}}+{{\rho }_{C}}+{{\rho }_{D}}=\]constant If we resolve \[{{\rho }_{A}},{{\rho }_{B}},{{\rho }_{C}}\] and \[{{\rho }_{D}}\] In horizontal and vertical directions, we find that initially \[\vec{p}={{\rho }_{A}}+{{\rho }_{B}}+{{\rho }_{C}}+{{\rho }_{D}}=0\] So, finally \[{{\rho }_{A}}+{{\rho }_{B}}+{{\rho }_{C}}+{{\rho }_{D}}=0\] \[{{\rho }_{A}}=0,\] \[{{\rho }_{B}}=-{{\rho }_{B}}\] \[{{\rho }_{C}}={{\rho }_{D}}\] or \[2{{\rho }_{C}}={{\rho }_{B}}\] \[2m{{V}_{C}}=m{{V}_{B}}=mv\] \[{{V}_{C}}=\frac{V}{2}\]
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