Question

When a ceiling fan is switched off, its angular velocity fall to half while it makes $36$ rotations . How many more rotations will be make before coming to rest ? (Assume uniform angular retardations ).

• A. $36$
• B. $24$
• C. $18$
• D. $12$

Answer 1

The correct option is D $12$

Using ${\omega }_2^2-{\omega }_1^2=2\alpha \theta$ ,

We get,

$(\frac{\omega }{2}{)}^2-{\omega }^2=2\alpha (36\times 2\pi )$........(i)

Similarly ,$(0{)}^2-(\frac{\omega }{2}{)}^2=2\alpha (\pi \times 2\pi )$.......(ii)

Dividing Eq.(i) by (ii), we get

$\frac{-\frac{3}{4}{\omega }^2}{-\frac{{\omega }^2}{4}}=\frac{36}{n}$

$n=12$