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

Answer: (C)

In first three seconds, angle rotated
$\theta =2\pi \times 10rad$
Using, $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$
$\therefore 2\pi \times 10=0+\frac{1}{2}\alpha \times 3^2=\frac{9}{2}\alpha$ ...(i)
For the rotation of fan in next three second, the total time of revolutions = $3+3=6s$
Let total number of revolutions = $N$
Then angle of revolutions, $\theta \prime =2\pi Nrad$
$\therefore 2\pi N=0+\frac{1}{2}\alpha \times 6^2=18\alpha$ ..(ii)
Dividing (ii) by (i), we get
$N=40$
No. of revolutions in last three seconds
= 40 - 10 = 30 revolutions