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