Question

A fan is running at $300\text{rpm}$. It is switched off. It comes to rest by uniformly decreasing its angular speed in $10$ seconds. The total number of revolutions in this period are :-

• A. $15$
• B. $25$
• C. $35$
• D. $30$

Answer 1

The correct option is B $25$

Angular speed of fan at $t=0$
${\omega }_0=300\text{rev/min}$
${\omega }_0=300\text{rev/min}=\frac{300}{60}\text{rev/s}=5\text{rev/s}$
Angular speed of fan at $t=10\text{s}$
$\omega =0$ (comes to rest)

From eqn. $\omega ={\omega }_0+\alpha t$
$\Rightarrow 0=5+\alpha \left(10\right)$
or $\alpha =-0.5{\text{rev/s}}^2$ ... (1)

From eqn. ${\omega }^2={\omega }_0^2+2\alpha \theta$
$0=(5{)}^2+2\times (-0.5{\text{rev/s}}^2)\times \theta$
or $\theta =25\text{rev}$