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
$\theta = 2 \pi \times 10 \, rad$
Using, $\theta =\omega_{0}t +\frac{1}{2} \alpha t^{2 }$
$\therefore \:\:\: 2\pi \times10 = 0 + \frac{1}{2} \alpha \times3^{2} = \frac{9}{2} \alpha$ ...(i)
For the rotation of fan in next three second, the total time of revolutions = $3 + 3 = 6\, s$
Let total number of revolutions = $N$
Then angle of revolutions, $\theta′= 2 \, \pi N\, rad$
$ \therefore \:\:\: 2\pi N = 0+\frac{1}{2} \alpha \times6^{2} = 18 \alpha$ ..(ii)
Dividing (ii) by (i), we get
$N = 40 $
No. of revolutions in last three seconds
= 40 - 10 = 30 revolutions