A) \[17\,N{{m}^{-1}}\]
B) \[21\,N{{m}^{-1}}\]
C) \[14\,N{{m}^{-1}}\]
D) \[27\,N{{m}^{-1}}\]
E) \[9\,N{{m}^{-1}}\]
Correct Answer: A
Solution :
Applying conservation of energy, \[\frac{1}{2}K{{x}^{2}}=\text{change}\,\,\text{in}\,\text{KE}\] \[=\frac{1}{2}m\left[ {{1}^{2}}-{{\left( \frac{1}{2} \right)}^{2}} \right]\] \[=\frac{1}{2}m\left[ 1-\frac{1}{4} \right]=\frac{1}{2}\times 2\times \frac{3}{4}\] \[\Rightarrow \] \[K\times {{(30\times {{10}^{-2}})}^{2}}=\frac{3}{2}\] \[\Rightarrow \] \[K\times 0.09=\frac{3}{2}\] \[\Rightarrow \] \[K=\frac{3\times 100}{2\times 9}=\frac{300}{18}\] \[=\frac{100}{6}=16.6\,N{{m}^{-1}}\]
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