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Question

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


A
143
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B
272
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C
314
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D
722
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Solution

The correct option is C $$314$$
Given angular retardation$$=4\ rad/s^2$$
          Angular velocity$$ = 1200\times \dfrac{2\pi }{60}rad/s$$
                                        $$=40\pi\  rad/s$$
 $$\therefore \omega^2=2\alpha \theta $$
   $$\Rightarrow \theta =\dfrac{\omega ^2}{2\alpha }=\dfrac{40\pi \times 40\pi }{2\times 4}=200\pi ^2$$
   $$Number\; of\: revolutions =\dfrac{\theta }{2\pi }=100\pi =314$$

Physics

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