A particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolu

Question

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 $	heta$ to the horizontal, the maximum height attained by it is equal to $4 R$. The angle of projection $	heta$ is then given by:\

Professor PC Thomas Classes · Answer

(b) : Radius $=R$, Time period $=T$ Max. height attained by projectile $=4 R$ $$\begin{equation*} T=\frac{2 \pi R}{v} \Rightarrow v=\frac{2 \pi R}{T} 	ag{i} \end{equation*}$$ $4 R=\frac{4 \pi^{2} R^{2}}{T^{2}} \frac{\sin ^{2} 	heta}{2 g}$\ from (i)\ $	heta=\sin ^{-1}\left[\frac{2 g T^{2}}{\pi^{2} R}ight]^{1 / 2}$\