A) 354
B) 490
C) 413
D) 620
Correct Answer: C
Solution :
\[{{\omega }^{0}}=2\pi \frac{720}{60}\] \[=24\pi \,rad/s\] \[\omega =2\pi \times \frac{2820}{60}=94\,\pi \,rad/s\] We know that, \[\omega ={{\omega }_{0}}+\alpha t\] \[=94\pi =24\pi +\alpha (4)\] \[\alpha =\frac{70\pi }{14}=5\pi \,rad/{{s}^{2}}\] \[\Rightarrow \] From\[\theta ={{\omega }_{0}}t+\frac{1}{2}\alpha {{t}^{2}}\] \[=24\pi \times 14+\frac{1}{2}\times (5\pi )\times {{(14)}^{2}}\] \[=336\pi +490\pi =826\pi \] \[\Rightarrow \]The number of revolutions \[=\frac{826\pi }{2\pi }\] =413 revolutions
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