An iron ball of mass m, suspended by a light inextensible string of length from a fixed point, 0, is shifted by an angle \[{{\theta }_{0}}\] as shown so as to strike the vertical wall perpendicularly. The ' maximum angle made by the string with vertical after the first collision, if e is the coefficient of restitution, is

• A. \[{{\sin }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\]
• B. \[{{\cos }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\]
• C. \[{{\tan }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\]
• D. Zero