A) The magnitude of momentum of the composite body is\[\sqrt{{{(mv)}^{2}}+{{(MV)}^{2}}}\]
B) The composite body moves in a direction making an angle \[\theta ={{\tan }^{-1}}\left( \frac{MV}{mv} \right)\]with \[+\text{ }ve\]X-axis.
C) The loss of kinetic energy due to collision
D) All of the above
Correct Answer: D
Solution :
[d] As no external force is acting momentum of the system remains conserved, i.e., \[{{\vec{P}}_{f}}=mv\hat{i}+mV\hat{j}\] |
\[|{{\vec{P}}_{f}}|=\sqrt{{{(mv)}^{2}}+{{(MV)}^{2}}}\] |
\[\Rightarrow \]\[\tan \theta =\frac{MV}{mv}\] |
Loss in \[KE==\Delta K\] |
\[=\frac{m{{v}^{2}}}{2}+\frac{M{{V}^{2}}}{2}-\frac{1}{2}\left[ \frac{{{(mv)}^{2}}+{{(MV)}^{2}}}{M+m} \right]\] |
\[=\frac{Mm}{2\,(M+m)}\times ({{V}^{2}}+{{v}^{2}})\] |
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