A) \[\frac{1}{2}m{{v}^{2}}\times \frac{m}{(m+M)}\]
B) \[\frac{1}{2}m{{v}^{2}}\times \frac{M}{(m+M)}\]
C) \[\frac{1}{2}m{{v}^{2}}\times \frac{(M+m)}{M}\]
D) \[\frac{1}{2}M{{v}^{2}}\times \frac{m}{(m+M)}\]
Correct Answer: A
Solution :
By the law of conservadon of momentum \[mv=(m+M)V\] \[\therefore \] \[V=\left( \frac{m}{m+M} \right)v\] \[\therefore \] Kinetic energy of composite block \[{{E}_{k}}=\frac{1}{2}(m+M){{V}^{2}}\] \[=\frac{1}{2}\frac{(m+M){{m}^{2}}{{v}^{2}}}{{{(m+M)}^{2}}}=\frac{1}{2}m{{v}^{2}}\left( \frac{m}{m+M} \right)\]
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