Question

When a ceiling fan is switched off, its angular velocity reduces to half its initial value after it completes $36$ rotations. The number of rotations it will make further before coming to rest is Assuming angular retardation to be uniform

• A. $10$
• B. $20$
• C. $18$
• D. $12$

Answer 1

The correct option is D $12$

1st case:

We can write the equation of motion for circular motion as:

${\omega }^2={\omega }_0^2+2a{\theta }_n$

Now, $\omega =\frac{{\omega }_0}{2},\theta =36\times 2\pi$ (given)

So, $\frac{{\omega }_0^2}{4}={\omega }_o^2+2\alpha \times 36\times 2\pi$

So, $\alpha =\frac{-3{\omega }_0^2}{4\times 144\pi }$

2nd case:

$0=\frac{{\omega }_0^2}{4}-2\times \frac{3{\omega }_0^2}{4\times 144\pi }\times \theta$

So, $\theta =24\pi$

So, number of rotations made by the fan before coming to rest $=\frac{24\pi }{2\pi }=12$