A) \[2\pi \text{ }rad\text{ }{{s}^{-2}}\]
B) \[60\pi \text{ }rad\text{ }{{s}^{-2}}\]
C) \[40\pi \text{ }rad\text{ }{{s}^{-2}}\]
D) \[90\pi \text{ }rad\text{ }{{s}^{-2}}\]
Correct Answer: A
Solution :
: Here, Initial angular speed of the wheel, \[{{\omega }_{0}}=1800\times \frac{2\pi }{60}\,rad\,\,{{s}^{-1}}=60\pi \,rad\,{{s}^{-1}}\] Final angular speed of the wheel, \[\omega =3000\times \frac{2\pi }{60}\,\,rad\,{{s}^{-1}}=100\pi \,rad\,{{s}^{-1}}\] Time during which this change of speed takes place, \[t=20s\] Let a be angular acceleration of the wheel. As \[\omega ={{\omega }_{0}}+\alpha t\] \[\therefore \] \[\alpha =\frac{\omega -{{\omega }_{0}}}{t}=\frac{100\pi -60\pi }{20}\,rad\,{{s}^{-2}}\] \[=2\pi \,rad\,{{s}^{-2}}\]
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