A) \[\sqrt{\frac{2}{3}}m{{u}^{2}}\]
B) \[\frac{3}{4}m{{u}^{2}}\]
C) \[\frac{1}{8}m{{u}^{2}}\]
D) \[\frac{1}{3}m{{u}^{2}}\]
Correct Answer: C
Solution :
[c] \[{{\vec{P}}_{i}}={{\vec{P}}_{f}}\] \[\Rightarrow mu\hat{i}+m\left( \frac{u}{2}\hat{i}+\frac{u}{2}\hat{j} \right)=\left( m+m \right)\left( {{v}_{1}}\hat{i}+{{v}_{2}}\hat{j} \right)\] Compare both side \[\Rightarrow {{v}_{1}}=\frac{3u}{4},{{v}_{2}}=\frac{u}{4}\] \[\Delta KE={{K}_{i}}-{{K}_{f}}\] \[=\frac{1}{2}m{{u}^{2}}+\frac{1}{2}m{{\left( \frac{u}{2}\sqrt{2} \right)}^{2}}-\frac{1}{2}\left( 2m \right)\left( \frac{9{{u}^{2}}}{16}+\frac{{{u}^{2}}}{16} \right)\] \[=\frac{m{{u}^{2}}}{8}\]
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