A) \[\frac{1}{2}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\frac{1}{2\sqrt{2}}\]
D) \[\frac{1}{4}\]
Correct Answer: B
Solution :
Fraction of KE lost in collision \[=\frac{\frac{1}{2}m{{u}^{2}}-\frac{1}{2}m{{v}^{2}}}{\frac{1}{2}m{{u}^{2}}}\] \[=1-{{\left( \frac{v}{u} \right)}^{2}}=\frac{1}{4}\] (given) \[v=u\sqrt{\frac{3}{4}}\] The ball strikes at \[{{45}^{0}}\] component of velocity parallel to wall \[(u\cos {{45}^{0}})\] will not change while component of velocity normal to wall will change. \[v=u\,\sqrt{\frac{3}{4}}\,={{\left[ {{\left( \frac{u}{\sqrt{2}} \right)}^{2}}+\,{{\left( \frac{eu}{\sqrt{2}} \right)}^{2}} \right]}^{1/2}}\] \[=u\,{{\left[ \frac{1}{2}\,+\frac{{{e}^{2}}}{2} \right]}^{1/2}}\]on solving \[e=\frac{1}{\sqrt{2}}\]
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