A particle moving in a circle of radius \(R\) with a uniform speed takes a time \(T\) to complete one revolution. If this particle were projected with the same speed at an angle ' \(\theta\) ' to the horizontal, the maximum height attained by it equals \(4 \mathrm{R}\). The angle of projection, \(\theta\), is then given by

1. A \(\theta=\cos ^{-1}\left(\frac{g T^{2}}{\pi^{2} R}\right)^{1 / 2}\)
2. B \(\theta=\cos ^{-1}\left(\frac{\pi^{2} R}{g T^{2}}\right)^{1 / 2}\)
3. C \(\theta=\sin ^{-1}\left(\frac{\pi^{2} R}{g T^{2}}\right)^{1 / 2}\)
4. D \(\theta=\sin ^{-1}\left(\frac{2 \mathrm{~g} T^{2}}{\pi^{2} R}\right)^{1 / 2}\)