• # question_answer Body of mass m moving with a velocity$v$in the $+\text{ }ve$X direction collides with a body of mass M moving with a velocity V in the $+\text{ }ve$Y direction. The collision is perfectly inelastic. Mark out the correct statement(s) w.r.t. this situation. 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

 [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 $KE==\Delta K$ $=\frac{m{{v}^{2}}}{2}+\frac{M{{V}^{2}}}{2}-\frac{1}{2}\left[ \frac{{{(mv)}^{2}}+{{(MV)}^{2}}}{M+m} \right]$ $=\frac{Mm}{2\,(M+m)}\times ({{V}^{2}}+{{v}^{2}})$