Q. When a ceiling fan is switched on, it makes 10 rotations in the first 4 s. How many rotations will it make in the next 4 s? (Assuming uniform angular acceleration)
A) 10
B) 20
C) 40
D) 30
Explanation
(d) $\theta = 2\pi n = \omega_{0}t + \frac{1}{2}\alpha t^{2}$
$2\pi \times 10 = \frac{1}{2}\ \alpha 4^{2}$ or $\alpha = \frac{40\pi}{16}$
Let it make $N$ rotations in the first 8 s
Then, $2\pi N = \frac{1}{2}\alpha\ 8^{2}$
or $N = \frac{1}{2\pi} \times \frac{64}{2} \times \frac{40\pi}{16} = 40$
$\therefore$ The required number of rotations
$= 40 - 10 = 30$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.