A particle is moving in a circle of radius $$R$$ with constant speed. The time period of the particle $$T$$ in a time $$t=\dfrac{T}{6}$$.
Correct option is C. $$\dfrac{2\pi R}{T}$$
We know that
$$\theta=2\pi t\ t=\dfrac{2\pi}{T}\times t$$
$$\Rightarrow \theta=\dfrac{2\pi}{T}\times \dfrac{T}{6}=\dfrac{\pi}{3}$$
average speed $$=\omega R=2\pi fR$$
$$=\dfrac{2\pi}{T}\times R=\dfrac{2\pi R}{T}$$