A) \[\frac{4n}{15}\]
B) \[\frac{8n}{15}\]
C) \[\frac{16n}{15}\]
D) \[\frac{32n}{15}\]
Correct Answer: C
Solution :
[c] : The angular velocity is given as \[{{\omega }^{2}}=\omega _{0}^{2}+2\alpha (\theta -{{\theta }_{0}})\]when the fan is switch off \[\theta =2\pi n,{{\theta }_{0}}=0,\omega =\frac{{{\omega }_{0}}}{4}\] \[{{\left( \frac{{{\omega }_{0}}}{4} \right)}^{2}}=\omega _{0}^{2}-2\alpha (2\pi n)\Rightarrow 2\alpha (2\pi n)=\frac{15}{16}\omega _{0}^{2}\] \[2\pi n=\frac{15}{16}\left( \frac{\omega _{0}^{2}}{2\alpha } \right)\]When the fan comes to rest \[0=\omega _{0}^{2}-2\alpha (2\pi n')\Rightarrow 2\pi n'=\left( \frac{\omega _{0}^{2}}{2\alpha } \right)\]or\[n'=\frac{16}{15}n\]
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