Q122 / 160 · JIPMER 2012 · Physics

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 ?

  • A
    10
  • B
    20
  • Correct answer
    C
    30
  • D
    40

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 $t=3 \mathrm{~s}$ to $t=6 \mathrm{~s}$ $\theta_{\text {lost }}=\theta_2-\theta_3=80 \pi-20 \pi$ $=60 \pi$ Number of revolution $=\frac{60 \pi}{2 \pi}=30$

Hence, the correct answer is option: 'C'.

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