A) 2v
B) \[2\frac{v}{\pi }\]
C) \[\frac{v}{2}\]
D) \[\frac{v}{2\pi }\]
Correct Answer: B
Solution :
We are given that a particle is moving with a constant speed v in the circle so the time taken to cover the complete circle would be equal to \[T=\frac{2\pi r}{v},\]hence the time taken to v cover half the rotation would be equal to \[{{T}_{1/2}}=\frac{2\pi r}{2v}=\frac{\pi r}{v},\]hence the magnitude of average velocity after half rotation would be equal to \[{{v}_{av}}=\frac{2r}{\frac{\pi r}{v}}=\frac{2v}{\pi }.\]
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