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A fan is rotating with an angular speed $300 \mathrm{rpm}$. The fan is switched off, and it takes $80 \mathrm{~s}$ to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is
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Verified Answer
The correct answer is:
200
As $\omega=\omega_0+\alpha \mathrm{t}$
$$
\begin{aligned}
& \Rightarrow \mathrm{f}=\mathrm{f}_0+\frac{\alpha}{2 \pi} \mathrm{t} \\
& \Rightarrow 0=5+\frac{\alpha}{2 \pi} \times 80 \\
& \Rightarrow \alpha=-\frac{10 \pi}{80}=-\frac{\pi}{8} \mathrm{rad} / \mathrm{sec}^2
\end{aligned}
$$
So, $\theta=\frac{1}{2} \times \frac{\pi}{8} \times 80^2$
$$
=400 \pi
$$
No. of revolution $=\frac{400 \pi}{2 \pi}=200$
$$
\begin{aligned}
& \Rightarrow \mathrm{f}=\mathrm{f}_0+\frac{\alpha}{2 \pi} \mathrm{t} \\
& \Rightarrow 0=5+\frac{\alpha}{2 \pi} \times 80 \\
& \Rightarrow \alpha=-\frac{10 \pi}{80}=-\frac{\pi}{8} \mathrm{rad} / \mathrm{sec}^2
\end{aligned}
$$
So, $\theta=\frac{1}{2} \times \frac{\pi}{8} \times 80^2$
$$
=400 \pi
$$
No. of revolution $=\frac{400 \pi}{2 \pi}=200$
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