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 $4R$. The angle of projection $\theta$ is then given by___

• A

  $\theta ={\cos }^{-1}{\left(\frac{g{T}^2}{{\pi }^{2}R}\right)}^{\frac{1}{2}}$
• B

  $\theta ={\cos }^{-1}{\left(\frac{{\pi }^{2}R}{g{T}^2}\right)}^{{}^{\frac{1}{2}}}$
• C

  $\theta ={\sin }^{-1}{\left(\frac{{\pi }^{2}R}{g{T}^2}\right)}^{{}^{\frac{1}{2}}}$
• Correct answer
  D

  $\theta ={\sin }^{-1}{\left(\frac{2g{ T}^2}{{\pi }^{2}R}\right)}^{\frac{1}{2}}$

Hence, the correct answer is option: 'D'.