Question

When a ceiling fan is switched on, it makes 10 rotations in the first 3 seconds. How many rotations will it make in the next 3 seconds (Assume uniform angular acceleration)

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

Answer: (C)

30

$\begin{array}{c}\text{Given-* ceiuing fan makes lo rotations in}3\sec \\ \text{let the angular acceleration of the fan be}\left(\alpha \right)\end{array}$

$\begin{array}{c}10\text{rotations}=10\times 2\pi =20\pi \text{radians}\\ \text{From the equation -}\\ \begin{array}{c}\theta ={\theta }_0+\frac{1}{2}\alpha t^2\\ 20\pi =0+\frac{1}{2}\alpha \times (3{)}^2\Rightarrow \alpha =\frac{40\pi }{9}\end{array}\end{array}$

$\begin{array}{c}\text{For next}3\text{seconds -}\\ \begin{array}{cc}\theta & =0+\frac{1}{2}\times \frac{40\pi }{9}\times \left[\right(6{)}^2-\left(3{)}^2\right]=60\pi \\ \theta =60\pi & =\frac{60\pi }{2\pi }\text{Rotations}=30\text{Rotations}\end{array}\\ \text{Hence, option (c) is correct.}\end{array}$