Question

When a ceiling fan is switched off, its angular velocity reduces to $50\%$ while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

• A. $18$
• B. $12$
• C. $36$
• D. $48$

Answer 1

Answer: (B)

${\left(\frac{{\left(\omega \right)}_0}{2}\right)}^2={\omega }_0^2-2\alpha {\left(\theta \right)}_1\Rightarrow 2\alpha {\left(\theta \right)}_1=\frac{3}{4}{\omega }_0^2$ ....(i)
$0={\left(\frac{{\left(\omega \right)}_0}{2}\right)}^2-2\alpha {\left(\theta \right)}_2\Rightarrow 2\alpha {\left(\theta \right)}_2=\frac{{\omega }_0^2}{4}$ ...(ii)
From (i) & (ii) $\frac{{\theta }_1}{{\theta }_2}=3$
$\Rightarrow {\theta }_2=\frac{{\theta }_1}{3}=\frac{36}{3}=12$ rotations