Question

A fan is running at $3000$ $rpm$ . It is switched off. It comes to rest by uniformly decreasing its angular spead uniformly in $10$ seconds. The total number of revolution in this period.

• A. $150$
• B. $250$
• C. $350$
• D. $300$

Answer 1

Answer: (B)

$250$

$\begin{array}{c}{\omega }_0=3000rad/min\\ {\omega }_0=\frac{3000}{60}rad/sec=50,t=10sec\\ {\omega }_f=0,{\omega }_f={\omega }_0+\alpha t\end{array}$

$\begin{array}{cc}\theta & =50-\alpha \left(10\right)\\ \alpha & =5\mathrm{vad}/{sec}^2\\ \theta & ={\omega }_{0}t+\frac{1}{2}\alpha t^2\\ \theta =50\times 10& +\frac{1}{2}\times -10\times {10}^2\\ \theta & =500-250=250revolution\\ \text{Option}B\text{is correct}& \end{array}$