Question

When a ceiling fan is switched off its angular velocity reduces to $50 \%$ while it makes $36$ rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)?

• A. 18
• B. 12
• C. 36
• D. 48

Answer 1

Answer: (B)

By using equation $\omega^{2}=\omega_{0}^{2}-2 \alpha \theta$
$\left(\frac{\omega_{0}}{2}\right)^{2}=\omega_{0}^{2}-2 \alpha(2 \pi n) $
$\Rightarrow \alpha=\frac{3}{4} \frac{\omega_{0}^{2}}{4 \pi \times 36},(n=36)$....(i)
Now let fan completes total $n^{\prime}$ revolution from the starting to come to rest
$0=\omega_{0}^{2}-2 \alpha\left(2 \pi n^{\prime}\right) $
$\Rightarrow n^{\prime}=\frac{\omega_{0}^{2}}{4 \alpha \pi}$
Substituting the value of $\alpha$ from equation (i)
$n^{\prime}=\frac{\omega_{0}^{2}}{4 \pi} \frac{4 \times 4 \pi \times 36}{3 \omega_{0}^{2}}=48 $ revolutions
Number of rotation $=48-36=12$