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. 12
• B. 18
• C. 24
• D. 54

Answer 1

The correct option is A 12

Let the initial angular velocity of the fan be $\omega$
$\therefore$ Its angular velocity when the fan makes 36 rotations (Given ${\omega }_1=0.5\omega$ ) using
${\omega }_2^2-{\omega }_1^2=2\alpha S$
where $S=2\pi \left(36\right)$ radian
$\therefore (0.5\omega {)}^2-{\omega }^2=2\alpha \times 2\pi (36)⟹4\pi \alpha =\frac{-0.75{\omega }^2}{36}$

Let the fan makes n more rotations before coming to rest.
Using ${\omega }_3^2-{\omega }_2^2=2\alpha S$
$\therefore 0-(0.5\omega {)}^2=2\alpha (2\pi n)$

(or) $-0.25{\omega }^2=\frac{-0.75{\omega }^2}{36}\times n$
$⟹n=12$