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
B
272
C
314
D
722

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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