A) \[\frac{7}{10}M{{V}^{2}}\]
B) \[\frac{1}{2}M{{V}^{2}}\]
C) \[\frac{2}{5}M{{V}^{2}}\]
D) \[\frac{10}{7}M{{V}^{2}}\]
Correct Answer: A
Solution :
: Kinetic energy of rolling sphere \[=\frac{1}{2}M{{V}^{2}}+\frac{1}{2}I{{\omega }^{2}}\] For sphere,\[I=\frac{2}{5}M{{R}^{2}}\]and\[R\omega =V\] \[\therefore \]\[KE=\frac{1}{2}M{{V}^{2}}+\frac{1}{2}\left( \frac{2}{5}M{{R}^{2}} \right){{\omega }^{2}}\] \[=\frac{1}{2}M{{V}^{2}}+\frac{1}{5}M{{V}^{2}}=\frac{7}{10}M{{V}^{2}}\]
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