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 $=48-36=12$