When a ceiling fan is switched on, it makes 10 revolution in the...

When a ceiling fan is switched on, it makes 10 revolution in the first 3 s. Assuming a uniform angular acceleration, how many rotation it will make in the next 3 s ?

Options

Correct answer

C. 30

Step-by-step solution

Angle turned in three second and

\theta_3 s=2 \pi \times 10=20 \pi \mathrm{rad} \theta_1=\omega_0 t+\frac{1}{2} \alpha t^2\alpha=\frac{49 \pi}{9} \mathrm{rad} / \mathrm{s}^2

Now, angle turned in 6 s from the starting

\theta_2=\omega_0 t+\frac{1}{2} \alpha t^2=0+\frac{1}{2} \times\left(\frac{40 \pi}{9}\right)+(6)^2 =80 \pi \mathrm{rad}

Angle turned between

t=3 \mathrm{~s}

t=6 \mathrm{~s}\theta_{\text{lost }}=\theta_2-\theta_3=80 \pi-20 \pi=60 \pi

Number of revolution

=\frac{60 \pi}{2 \pi}=30

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