# A particle is moving in a circle of radius 𝑅 in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at 𝑡 = 0 is 𝑣0, the time taken to complete the first revolution is

Question: A particle is moving in a circle of radius 𝑅 in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at 𝑡 = 0 is 𝑣0, the time taken to complete the first revolution is

(A) $\dfrac{R}{v_{0}}$

(B) $\dfrac{R}{v_{0}}\left( 1-e^{-2\pi }\right)$

(C) $\dfrac{R}{v_{0}}e^{-2\pi }$

(D) $\dfrac{2\pi R}{v_{0}}$