Question

When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest?

• A. 24
• B. 36
• C. 18
• D. 12

Answer 1

The correct option is D 12

From third equation of angular motion
${\omega }^2={\omega }_0^2-2\propto \theta$
[Here, $\omega =\frac{{\omega }_0}{2},\theta =36\times 2\pi$]
$\therefore {\left(\frac{{\omega }_0}{2}\right)}^2={\omega }_0^2-2\alpha \times 36\times 2\pi$
or $4\times 36\pi \alpha ={\omega }_0^2-\frac{{\omega }_0^2}{4}$
or $4\times 36\pi \alpha =\frac{3{\omega }_0^2}{4}$
or $\alpha =\frac{{\omega }_0^2}{16\times 12\pi }$ .......(i)
According to question again applying the third equation of angular motion
${\omega }^2={\omega }_0^2-2\alpha \theta$ [Here, $\omega =0$]
$\therefore 0={\left(\frac{{\omega }_0}{2}\right)}^2-2\times \frac{{\omega }_0^2\cdot \theta }{16\times 12\pi }$
or $\theta =24\pi$ or $\theta =12\times 2\pi$
But $2\pi =1$ cycle
So, $\theta =12$ cycle