A) 12.5%
B) 25%
C) 50%
D) 75%
Correct Answer: D
Solution :
We know that \[e=\frac{{{v}_{1}}-0}{v-0}=\frac{{{v}_{1}}}{v}\]or \[0.5=\frac{{{v}_{1}}}{v}\] or \[{{v}_{1}}=0.5\,v\] Percentage loss in KE is given be: \[\left[ \frac{\frac{1}{2}m{{v}^{2}}-\frac{1}{2}mv_{1}^{2}}{\frac{1}{2}m{{v}^{2}}} \right]\times 100=\frac{{{v}^{2}}-{{(0.5\,v)}^{2}}}{{{v}^{2}}}\times 100\] \[=\frac{3}{4}\times 100=75%\] Hence, the correction option is [d].
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