A) remain constant
B) increase by a factor of 2
C) increase by a factor of 4
D) decrease by a factor of 2
Correct Answer: C
Solution :
Initial kinetic energy of mass \[{{K}_{initial}}=\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}(m{{r}^{2}}){{\omega }^{2}}=\frac{1}{2}m({{r}^{2}}{{\omega }^{2}})\] \[=\frac{1}{2}mv_{0}^{2}\] Conservation of angular momentum \[m{{\upsilon }_{0}}{{R}_{0}}=m\upsilon \frac{{{R}_{0}}}{2}\Rightarrow \upsilon =2{{\upsilon }_{0}}\] Final kinetic energy of mass \[{{K}_{final}}=\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{(2{{v}_{0}})}^{2}}=4.\frac{1}{2}mv_{0}^{2}=4{{k}_{initial}}\]
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