$A$ particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal,the maximum height attained by it is equal to $4 R$. The angle of projection $\theta$ is then given by :

• A
  $\sin ^{-1}\left[\frac{2 g T^2}{\pi^2 R}\right]^{\frac{1}{2}}$
• B
  $\sin ^{-1}\left[\frac{\pi^2 R}{2 gT^2}\right]^{\frac{1}{2}}$
• C
  $\cos ^{-1}\left[\frac{2 gT^2}{\pi^2 R}\right]^{\frac{1}{2}}$
• D
  $\cos ^{-1}\left[\frac{\pi R}{2 g T^2}\right]^{\frac{1}{2}}$