Question

A fan is rotating with angular velocity $100rev/sec$. Then it is switched off. It takes $5$ minutes to stop. Find the total number of revolution made before it stops. (Assume uniform angular retardation)

• A. $12000$
• B. $15000$
• C. $20000$
• D. $6000$

Answer 1

The correct option is B $15000$

Answer is B.
In this case, the initial angular velocity of the fan is ${\omega }_0=0$ and the final angular velocity of the fan is $\omega =100rev/sec$.
The total number of revolutions before the fan coming to stop is calculated as follows.
$\theta =\left(\frac{\omega +{\omega }_0}{2}\right)t=\left(\frac{100+0}{2}\right)\times (5\times 60)=15,000rev$
Hence, the total number of revolution made before it stops is $15,000rev$.