Q108 / 150 · MHT CET 2011 · Physics

A wheel has a speed of 1200 revolutions per minute and is made to slow down at a rate of $4 \mathrm{rad} / \mathrm{s}^{2}$. The number of revolutions it makes before coming to rest is

  • A
    143
  • B
    272
  • Correct answer
    C
    314
  • D
    722

Solution

$\omega^{2}=\omega_{0}^{2}-2 a \theta$ $$ \begin{aligned} 0 &=4 \pi^{2} n^{2}-2 a \theta \\ \theta &=\frac{4 \pi^{2}\left(\frac{1200}{60}\right)^{2}}{2 \times 4} \\ &=200 \pi^{2} \mathrm{rad} \\ \therefore \quad 2 \pi n &=200 \pi^{2} \\ n &=100 \pi=100 \times 3.14 \end{aligned} $$ $=314$ revolution

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

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