A) \[{{\left( \frac{6\pi }{5} \right)}^{1/3}}\]
B) \[{{\left( \frac{3\pi }{10} \right)}^{1/3}}\]
C) \[{{\left( \frac{2\pi }{5} \right)}^{1/2}}\]
D) \[{{\left( \frac{6\pi }{13} \right)}^{1/3}}\]
Correct Answer: A
Solution :
\[\frac{d\omega }{dt}=10t\] \[\int_{0}^{\omega }{d\omega }=\int_{0}^{t}{10}tdt\] \[\omega =5{{t}^{2}}\] \[\int_{0}^{2\pi }{d\theta }=\int_{0}^{{{t}_{0}}}{5}{{t}^{2}}dt\] \[2\pi \frac{5t_{0}^{3}}{3}\] \[{{t}_{0}}={{\left( \frac{6\pi }{5} \right)}^{1/3}}\]
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