A) \[354\]
B) \[490\]
C) \[413\]
D) \[620\]
Correct Answer: C
Solution :
\[{{\omega }_{0}}=2\pi \times \frac{270}{60}\] \[=24\pi \,rad/s\] \[\omega =2\pi \times \frac{2820}{60}=94\pi \,rad/s\] We know that, \[\omega ={{\omega }_{0}}+\alpha t\] \[94\pi =24\pi +\alpha (14)\] \[\alpha =\frac{70\,\pi }{14}=5\pi \,rad/{{s}^{2}}\] \[\Rightarrow \] 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 \[=\frac{826\pi }{2\pi }\] \[=413\text{ }revolutions\]
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