Question

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

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

Answer: (C)

30

Answer 2

Angle turned in three second

$\theta_{3s} = 2\pi \times 10 = 20\pi$ rad

From $\theta = \omega_{0}t + \frac{1}{2}\alpha t^{2}$

⇒ $20\pi = 0 + \frac{1}{2}\alpha \times (3)^{2}$⇒ $\alpha = \frac{40\pi}{9}rad/s^{2}$

Now angle turned in 6 sec from the starting

$\theta_{6s} = \omega_{0}t + \frac{1}{2}\alpha t^{2} = 0 + \frac{1}{2} \times \left( \frac{40\pi}{9} \right) \times (6)^{2} = 80\pi\mspace{6mu}\mspace{6mu} rad$

\ Angle turned between t = 3s to t = 6s

$\theta_{\text{ 3 s}} = \theta_{6s} - \theta_{3s} = 80\pi - 20\pi = 60\pi$

Number of revolution$= \frac{60\pi}{2\pi} = 30$