When a ceiling fan is switched off, its angular velocity falls to (1/3) rd while it makes 24 rotations. How many more rotations will it make before coming to rest? (a) 3 (b) 6 (c) 9 (d) 12

Answer: (a). Use ω² = ω₀² - 2αθ with θ in rotations. First stage: ω₀² - (ω₀²)/(9) = 2α(24) ⇒ 8/9ω₀² = 48α Second stage: (ω₀²)/(9) = 2α n Divide: 1/8 = n/24 ⇒ n = 3 So the answer is (a) 3.

When a ceiling fan is switched off, its angular velocity falls to… | MHT CET 2025 (19 Apr, Shift 1)

Q7MHT CET 2025 · 19 APR · SHIFT 1Medium

Non-Uniform Circular Motion

When a ceiling fan is switched off, its angular velocity falls to $\left(\frac{1}{3}\right)$ rd while it makes 24 rotations. How many more rotations will it make before coming to rest?

Show answer and solution

Answer: (a)

Use $\omega^2 = \omega_0^2 - 2\alpha\theta$ with $\theta$ in rotations.
First stage: $\omega_0^2 - \frac{\omega_0^2}{9} = 2\alpha(24) \Rightarrow \frac{8}{9}\omega_0^2 = 48\alpha$
Second stage: $\frac{\omega_0^2}{9} = 2\alpha n$
Divide: $\frac{1}{8} = \frac{n}{24} \Rightarrow n = 3$
So the answer is (a) 3.

Report a mistake

Non-Uniform Circular Motion question from MHT CET 2025 (19 Apr, Shift 1)

More questions on Non-Uniform Circular Motion