Question

When a ceiling fan is switched on, it makes 10 revolutions in the first 3 seconds. Assuming a uniform angular acceleration, how many rotations it will make in the next 3 seconds?

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

The correct option is C 30

According to the question

Ceiling fan makes 10 revolutions in the first 3 seconds
${\theta }_1=2\pi \times 10=20\pi$ radian

Using equation of motion for circular motion
Using $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$
$20\pi =\frac{1}{2}\alpha \times 3\times 3\alpha =\frac{40\pi }{9}{\text{rad s}}^{-2}$

Now,
Angular velocity at the end of 3 s

${\omega }_1={\omega }_0+\alpha t=0+\frac{40\pi }{9}\times 3=\frac{40\pi }{3}{\text{rad s}}^{-1}$
If ${\theta }_2$ represents the angular displacement from 3 s to 6s, then
${\theta }_2={\omega }_{1}t+\frac{1}{2}\alpha t^2=\frac{40\pi }{3}\times 3+\frac{1}{2}\times \frac{40\pi }{9}\times 9=60\pi$
Number of rotations $=\frac{60\pi }{2\pi }=30$.

Hence the number of rotations is 30.